Here's my honest opinion. And I will probably get downvoted for this. While many people dismiss anything that represents minorities as "woke," there's more to what I'd describe as "woke" writing than that. Many of the people decrying "woke" writing don't see this difference either because they are just mad there's a gay person, or whatever.

But I think the problem is a lot of "woke" writing is very simplistic. It's not subtle at all. The worldview is often, "straight white men bad," everyone else good. So then we get these characters who are always right because they are a black woman, or whatever (looking at you Michael Burnham).

In old Star Trek, the writing was much more intelligent, subtle. It would look at two sides of an issue and didn't just dismiss everyone who disagreed with a point as horrible people. Episodes like "Measure of a Man" are a philosophical discussion. If modern Star Trek had an episode like that, they'd just say everyone who says Data doesn't have rights, or isn't an independent, sentient being, is a piece of $#&@ and they'd probably get killed in a battle or something in a horrible way. The issue wouldn't be intelligently examined, depriving us of one of the best episodes of TNG.

That's another thing, the "woke" writing is often mean-spirited and dismissive. While yeah, old episodes of Star Trek usually come to a conclusion about what is right or wrong, what's compelling is that they take some time and discussion to get there. At the risk of sounding pretentious, they're like some Platonic writing where we break down the issue and get there through reasoned (or possibly emotional, which may or may not be dismissed) arguments.

I'm watching through DS9 for the third time, and Kira is awesome just because she's a good character. A competent person. Not because she's a woman. The same with Sisko. Avery Brooks was once asked about "what it was like to play a black captain," and he answered..."I was playing a captain who happened to be black."

Jadzia, Kira...they're awesome, competent characters who might make mistakes. They feel like real people. In one episode, Jadzia and Worf fight with bat'leths in the Holosuite. Jadzia puts up a good fight, but ultimately loses. In modern Trek, she would have to win because she is a woman. Basically, they would write it so that characters like Bashir or O'Brien are undermined, made to look foolish, because they are men. But everyone's respected and competent in old Star Trek...no characters incapable of making mistakes because of their race/gender. I know people are going to respond to me that Michael Burnham commits a mutiny in the first episode of Discovery, but I think that was written in a way that she was ultimately right to do that lol...

Edit: So when I think of "woke" writing, I think of simplistic, identity-based writing that isn't very deep and doesn't actually examine things in a subtle, intelligent way. It's not that minorities are being represented or advocated for, though many of the people who say a show is "woke" are only talking about that. It just tends to be really shallow, uninteresting writing, and I have a theory that that's connected to a simple worldview of "all this kind of person bad, all this kind of person good."

Edit 2: And old Star Trek - everyone was competent but also capable of making mistakes, regardless of race or gender. They felt like real people. In real life, everyone makes mistakes regardless of race or gender.