(Note, I can't wait for Martin to end ASoIaF without telling us great King Bran's tax policy, then we get to bitch at him about it). Also, I'm very sorry for the length of this.
I've thought and talked over the whole Pullman thing with my partner, and she's of the mind that Pullman's women are... well, actually pretty poorly done. I agree, of course, but she made a good point that while Pullman might go on and on about women having sexual power and such, the two instances where the main female characters have sex (or make out with someone) is immediately punished. In one of the Sally Lockhart books, the titular character finally boinks her long term love interest. Almost immediately after there is a fire and, get this, he dies. In a fire. Also, surprise, she's pregnant! At the end of the His Dark Materials series, Lyra gets her crush on with her crush and they make out. But then for cosmic blah di blah they have to be separated so no sex for them. Also, where she used to be able to intuitively understand the compass, now that she wanted to boink a guy she has to study it to be able to understand it.
Because sex and horniness makes you lose something and you have to be punished for it. Interesting, Pullman.
And to add to that, the badass warrior women are those witches, who (or which, eh?) are basically Pullman's idea of Elves. Live a long time. Fly around. All women. But there is still the idea that they'd need to give up their witchiness to be with a human male long term (not entirely unlike Arwen or Luthien, but very unlike Elwing and Idril Celebrindal (who both boinked human or human hybrids and got to keep their elfiness)).
And then there is Mrs. Coulter, the kid killer, who is a classic femme fatale (you know, woman power, right Pullman?). She (like Lyra in later stories, apparently) may seem all aloof but she secretly really does want to be a mother. She's really got that motherly instinct, you know? Also, her crowning moment of redemption is when she uses her sexual wiles to trick Metatron into a trap with her whole "I'll give you what you want and then we'll bang, ok?" schtick. She also does it to save her child, of course. Okay, female sexual power then, hmm?
Now, for Lord of the Rings... yes, not a lot of ladies in it, but there are some. Eowyn is probably the primary human woman character, and she's undoubtedly badass. Also, the "thirst" for Aragorn is painfully painfully obvious, and her motivations are at least a little more complex than many of the other characters. There is also that chatty nurse lady who can't stop talking, but her chatter saves Faramir, Eowyn, and Merry's life. Her allegedly more learned male counterpart is also shown to be fucking useless, as he's got the whole "I'm a smart man who will now mansplain shit to you because I'm so smart" but he has nothing much to add. Or as Aragorn says: "Then go to the house of some man less learned but more wise who might still have some of the damn plant I need!"
Overall though, yes, not a lot of women in Lord of the Rings, and certainly not in The Hobbit.
Shelob is an interesting example, but even there she is somewhat independent of Sauron. She at least does her own thing. Sauron refers to her as his cat, more or less, but "she owns him not". Which is an interesting choice of words.
But now I'm going to go into the Silmarillion because I can. Here there are a lot more female characters, though to be fair they are often in more feminine associated roles. Melian the Maia is Queen of Doriath, and the source of the magic that protects it, but she's not the primary decision maker, and often her advice is ignored by her husband (and others). Of course, the ignoring of that advice results in horrible things happening, but hey. Really, her only problem is she didn't put her foot down more, as the only time she did put her foot down was when their daughter was acting up and her husband was being a shithead about it so she refused to give him any help with the mess he had caused (by, again, not fucking listening to her).
Galadriel learns a lot from Melian, a fact fully asserted in the text, but I think both Galadriel and her husband Celeborn learned from Melian and Thingol's mistakes. That is, if your wife is smarter than you, fucking listen to her, or better yet, let her make the damn decisions. Some might say Celeborn is whipped, but in reality he's being smart. He can do the administrative shit, and Galadriel can do the big decision making stuff, and overrule him when he's being racist against the Dwarves (or any other time she feels like).
Idril Celebrindal is an Elf who realizes her cousin has the hots for her, and feels really icky about it. But then this really hot human man shows up, and she's much more interested in the human. She's also the one who realizes shit is not going to go very well because her father, the king of Gondolin, has decided to ignore a very pertinent warning from the Vala Ulmo. So she takes the initiative and has an escape tunnel made, but wisely tells neither her father nor her creepy cousin about it. She marries the human, has a kid, and they are all able to escape Gondolin with a bunch of survivors when Morgoth's armies finally find and attack it (because of her creepy cousin). Also, her husband despite being a human ends up being counted as an Elf, allegedly, so she doesn't end up like Luthien or Arwen.
Speaking of that creepy cousin, his mom ended up in a rather sad abusive marriage, and that is how he came about. I'm fairly sure Tolkien was advocating for divorce with this bit here, because father was like son: a creepy bastard. Not sure how family values that situation was, considered it ended up as an attempted, then successful, murder-suicide. Daddy got a bit possessive over his son, and decided they would both die, but ended up killing the mom instead. No wonder the kid turned out fucked in the head.
There was also the case of Turin and the accidental incest. That was... fucked. I suppose the moral of that story was that dragons are shitheads.
As for human women... there was Haleth of the Haladin. Her husband and sons get murdered by orcs. She takes over the leadership of her people, helps kill the orcs, then leads them on a long ass exodus and eventually settles them in somewhere relatively safe (or at least, it lasted longer than most human places). She got them through some really tough spots too. She was so influential that her people were no longer called the Haladin but rather "The People of Haleth".
There was a human woman and an Elf Prince who fell in love too, but that didn't work out. She was able to hold her own in debate with the Elf Princes though, which is pretty neat, even if she was wrong on a few points.
But the most interesting case for me is Luthien, who has more feminist in her character than all of Pullman's bullshit. It's the same old "elf-angel hybrid chick meets neat human dude" story, except it plays out a bit differently. First off, while Beren falls in love with her almost immediately, they spend quite some time secretly "dating" before being revealed to her parents (Thingol and Queen Melian, as noted above) because some incel with a crush on her spied on her and sold her out. She forces her father to promise not to kill the guy, and instead of doing a walk of shame when he comes in, she shows him off like he's some kind of prince (Thingol does not like humans at this point). Beren asks to marry her, and she's made up her mind obviously enough, but daddy has none of it. And, ignoring his wife's advice (of bloody course), he says Beren can totally marry Luthien... IF he brings him a shiny rock. Specifically, one of the three shiny rocks Morgoth (the devil, essentially) has on his iron crown. Thingol figures he can get Beren killed that way, because it's impossible. Right? Beren is all like: "What, you'd sell your daughter for so cheap a thing as a shiny rock? You Elf kings are weird, man. But sure, I'll go do that." He knows he's probably going to die, but puts on a brave face. So he goes to do that and try to get some help from an Elf Prince that owes him a favour.
Beren has a grand old time getting Finrod Felagund, Lord of Nargothrond, one of the high princes of the Noldor (and distant relative of King Thingol) to help out. Unfortunately, the other elves of Nargothrond aren't keen on a suicide mission, and two of the sons of Feanor, Celegorm and Curufin, figure that their family is the only ones who deserve those shiny rocks so they sabotage the endeavour. So off goes Finrod and Beren and a few other Elves loyal to Finrod. They get caught by Sauron, you know, that guy, and tossed in a dungeon while he tries to figure out who this obviously important Elf Prince actually is.
Luthien gets word of this and decides to do something about it. Thingol, of course, has Luthien shut up in a treehouse a la Rapunzel. It is around this point that Melian pointedly stops giving Thingol advice beyond "Should have listened to me." Luthien, knowing quite well what she wants isn't putting up with daddy being an idiot, so she magically grows her hair out long, weaves it into a cloak of shadows (she had dark hair... I think Tolkien had a type), and uses the remnants of the hair as a rope to escape the tree. She puts her guards to sleep with said magic cloak of shadows and gets the fuck out of Doriath on her own initiative. She has a run in with the two principle douchebags of this story, Celegorm and Curufin, who are able to catch her thanks to their super magic hunting hound named Huan. They lock her up and send messages to Thingol being all like: "We got your daughter, how about Celegorm marries her and you do what we say, yeah?"
Luthien has that Disney Princess shit down pat, though, and being lonely she talks to the magic dog, who decides his master Celegorm is being an asshole so he helps her out. Not only does he break her out of the prison Celegorm shut her in, he takes her over to where Sauron is hanging out with his werewolves (Sauron... has a thing for werewolves). Luthien and a magic dog outsmart and outfight Sauron (who tries to fight the dog on its own terms by turning himself into a big ass werewolf, which turns out to be a big mistake. Furry: never even once), doing what one of the great Princes of the Noldor fail to do.
Oh and also, Finrod Felagund breaks his shackles and wrestles a werewolf to the death, killing it with his hands and teeth before he himself dies. Fucking metal. Also, yes, Thingol gets some of his family killed by being a fucking idiot and not listening to his wife, who, I remind everyone, is much smarter than him.
So Beren and Luthien are reunited and happy, the dog goes back to Celegorm, and all is great for a bit. Until Celegorm and his brother try to kill Beren and Luthien, but get their asses kicked. The dog also decides that going back to Celegorm was probably a mistake, and chases the two Elves off. The three of them eventually decide to solve this shiny rock problem. Luthien is all up for eloping and saying: "eh, fuck it". She doesn't care. Beren would feel bad about it though. He was determined to try to get her father on side, since it was the right thing to do unless utterly necessary to not. And he didn't want to separate Luthien from her family like that, I guess. I'll point out, though, that Tolkien does leave the idea of elopement on the table as occasionally, potentially, worth it. So yeah, very family values, but not totally so.
Long story short, Luthien does the heavy lifting to get past the massive werewolf at the gates of Morgoth's fortress, then she also does the heavy lifting when confronting Morgoth. Now, here is where something interesting happens. Remember how Pullman has that woman sexuality power shit that Mrs. Coulter Femme Fatales Metatron with? Something bizarrely similar happens here. Luthien knows Morgoth wants to possess her, but she also knows Morgoth has a soft spot for shiny pretty shit (see those shiny rocks he stole and now wears on his iron hat despite the fact they burn him). She offers her service to him as a minstrel and dancer. Morgoth is not really fooled, but he's so secure in his mighty power, in this the center of his domain, that he deigns to let her perform (and she is really quite pretty and shiny). So she dances, just as she had danced in the forests when Beren first saw her, but in her dancing she weaves a great spell of sleep over his whole court, but she cannot overcome him. Not just then. Then as she dances she vanishes, and Morgoth's eyes search for her... until she appears in front of his head, whaps him in the face with her sleep cloak, and thonk he falls from his throne asleep. Beren cuts one shiny rock from the iron crown, but his knife breaks when he tries for a second and it cuts Morgoth's cheek, prompting him to start waking up. So they get the fuck out.
Beren gets his hand bitten off by the now awake werewolf at the entrance, but the wolf goes crazy because that was the hand with the shiny magic rock in it. They get saved by eagles, Beren and Luthien return home to Doriath. Beren claims he has achieved his goal, since he technically said he'd have a silmaril in his hand when he returned... and technically, he did. Just in the hand that was now in the belly of the angry wolf that was attacking Doriath. Thingol realizes he's been a shithead, though, and they go to kill the big wolf. Huan shows up for it too, of course, and he and the wolf kill each other. Now shiny gem belongs to Thingol. Beren is killed saving Thingol though. Luthien dies of grief.
Luthien goes to where dead Elves go (and humans go briefly), but is able to sing so sad a tale that the Vala Mandos (elf-Hades... his name is Namo, really, but his halls are called Mandos, and so they all call him Mandos too) decides to let both her and Beren go back if she chooses to be human and so eventually die like humans do. There was another option, but she obviously didn't pick it. So bam, they're alive again in Doriath and hooray. Notably, that is the only time that Mandos has ever relaxed his rules for anyone.
So no, Luthien does not go around murdering things with a sword (like Eowyn, or maybe Haleth, though I suspect Haleth would more favour an axe). But she knows what she wants, she uses her agency to get that thing, and she insists on being involved when people like her father and even Beren (who wants her to stay safe) try to sideline her. Sure, the thing she wants is to marry this Beren guy, but so what? That's the motivation of so many heroes in stories, and at least it's on both sides here. Furthermore, at least this isn't a guy she never met before. She did get to know him over time before she was ratted out by that incel minstrel "nice guy", after all. She's a far more interesting, and more powerful, female character than Mrs. Coulter despite having a similar scene were the archvillain lusts for her and so brings about his own failure.
"Tolkien afraid of women." Bullshit. I'll argue that Tolkien's works were more feminist than Pullman's works any day. The only people to go mad and kill themselves when they don't get a shiny rock in Tolkien's work were men. Not so with Pullman.
Lord of the Rings does tick a few of the fascism boxes though, that's true. It uses a mythic style, and the Nazis and co. really liked appropriating that. Chiefly, though, is this talk of "blood". The "blood" of Numenor "is all but spent". So on and so forth. There is also the idea of categories. High Men, Middle Men, Low or Twilight Men. It gets a bit... worrisome. "Black troll-men from Far Harad"... yeeeeeeaah. But Tolkien funnily enough did not really make the Numenoreans all that great seeming all the time, and he gets pretty pissy with Numenoreans being so past obsessed. Minas Tirith is a kind of bleak place, with little plant life of note. They were more obsessed with legacy and the past, with tombs getting more attention than the living and families at points. An obsession with ancient lore and such somewhat dooms the Numenoreans, and it is only by mingling with the more hardy peoples that they really stay around. There is a sense that for all the bluster of the Gondorians, the peoples of its provinces, often more swarthy and such than the High Lords of Minas Tirith, are the ones with whom the nation's true hope and future lies. It was in the mingling of peoples that hope could be found.
There was a civil war in Gondor once when a prince married one of those, ugh, Rohirrim people, and then he was going to become king. Couldn't have that; it would dilute the purity of the bloodline and increase the rate of decline in said bloodline! Well, big civil war, the blood purity people lose horribly, and guess what? The decline continues... as normal. It turns out it wasn't "blood purity" that meant a damn, but yes, the greater sense of a marred world in decline. Very veeeery Catholic, that. No arguing LotRs isn't Catholic as fuck, because it is. Definitely.
But in terms of family values, you could be very right about that. But I'm not so sure. Tolkien was a bit of a funny man, and he seems to have subverted quite a few expectations in his day. He'd still probably be conservative in mindset, but I don't know.