If you want a detailed explanation of the Amazon show, I did it in this post here but the short answer is it's actually good and not really woke at all.
This post is more discussing a something that looks to be the future of the franchise in terms of lore so there will be spoilers for the show.
Basically in the show, ALL lore related to Fallout New Vegas has been erased. The fractions are either not mentioned at all or severely diminished in terms of the NCR, some things in 1 and 2 have been changed (like Vault 15 which Shady Sands was built around is not mentioned at all) and it looks like they are only using the setting of New Vegas in a season 2 as they show the strip at the end of the season.
This is one thing, but I also recently heard of a Fallout 4 update and DLC planned where the update is optimising for 'next gen' consoles and the free DLC will introduce a new fraction to the commonwealth to stop...
..the fucking Enclave...
They seem to be only keeping lore cannon completely in Fallout 3 and 4 so does the Legion exist any more? Are the Followers of the Apocalypse still around or they gone too? Does any of the characters we liked from New Vegas exist either like Boone, Veronica or Cass?
The other thing that urks me is Fallout New Vegas was the best written and world built game in the franchise in competition with 1 and 2. The fact they are bringing back the Enclave for 4 just makes me think the writing staff at Bethesda aren't that creative at all and they're just rehashing old plots again and again than try some other direction or a new take on an old fraction. It's REALLY not giving me hope for Elder Scrolls 6...
TDLR: Bethesda may be doing what Disney did to Star Wars Extended Universe and erasing lore not made directly with Bethesda
Ok, what is woke then?
The two main characters who we might think of as woke inserts are shown to be constantly incompetent, surviving by sheer plot armour. Lucy is TOO naive and she pays for it everytime while Maximus is too weak willed at times and constantly makes the wrong decisions.
The most competent, likable character is Cooper the ghoul who is white and the biggest bad? His Black wife who proposed turning vaults into experiments.
That's episode 6 or 7, how did you see that scene when you couldn't watch after episode 2?
There are plenty of the usual tells. Be it the white woman/black man pairing or male characters being idiots while female characters being far more competent. It may not be in your face woke but it is just as woke as for example Rings of Power.
EDIT: Completely forgot the ftm non-binary actress/character who is referred to as "their" in the show.
Because someone uploaded the scene.
After Knight Titus turned out to be a complete buffoon with a bored and annoying voice saying "Oh fuck. Oh fuck." I was done with the show. I could have ignored the woke elements but not the terrible writing, costumes, CGI and non existent attention for detail.
The most competent character in the whole series is a white man.
I'm going to redirect you two comments down. Besides woke media has a tendency to be so badly written that the supposed hero is actually a complete buffoon.
The supposed hero, the white woman, largely is a complete buffoon through the series.
I feel like you're really reaching when the most competent characters are white, Cooper and the Lucy's brother.
As for female, let's go down the list:
Main bad guy/leading NCR remnants: essentially gave Cold Fusion technology to the Brotherhood
Betty: easily duped by Lucy's Brother
Cooper's wife: despite planning the great war, didn't have her daughter in safe place before bombs fell
Ironically the most competent bad guy is Lucy's father who manipulates Lucy and Maximus easily and it's only Cooper that easily sees through his BS.
Hell most of the guys that die are because of Lucy's naivety like those guys selling organs, unless you want to argue a Barbie where their messaging Ironically gets the opposite of what they wanted to convey, I really don't see it.
Woke isn't just about what character is competent or not. But if that's what you define as woke then sure Fallout isn't woke at all.