I think you're missing the key detail.
""woke" is supposed to mean "aware of inequalities in our society""
You're missing the part that "woke" implies the rest of the population is "asleep".
And this isn't just a clever play on words, it's quite literally the problem.
Let me be clear, "woke" as I determine it is not about diversity. I never had any issue with any Discovery characters. I only saw a bit of Adira, saw none of Gray. And as for Stamets and Culber, even though I knew by then that Disco wasn't my Trek flavor of choice, I made a special point of watching the episode where Culber was brought back. The creators of Trek felt that under Berman, the LGBT+ community had been underrepresented, and they wanted to fix that. And in any case, the other nu Treks all have diverse cast members. "Lower Decks" even has an LGBT lead.
The problem with whining about "wokeness" and being upset that "wokesters" think you're "asleep" is that it requires you to believe that institutional inequality does not embed itself into our society in ways that the majority does not always perceive.... in a world where the infant mortality rate for black folk is significantly higher than it is for white folk, and where we all have implicit biases we're not even always aware of.
Like, sorry dude, but sometimes we are biased in ways that are unfair and we deserve to be called out for
If a person feels that any sentiment I express is unfair, and chooses to discuss this with me politely, rationally, and non-abusively, I will consider their position, and any evidence they choose to share. I make no promises to adopt it, though.
However, if that same person responds with potty-words, insults, forced silencing, or other bullying tactics, I will not consider their position. Justify it as hate speech or any -ism or -phobia you want... in 1950, it was "un-American activities". The fiddlers might be on the opposite side of the political spectrum, but the dance is the same.
The reason I proudly declare myself "un-woke" is because in a world where accused witches are being burned, I would rather not associate myself with the people building the bonfires.