system
A chat on subreddit /r/NoStupidQuestions
human
Woke does not carry around a positive connotation from the Right and the I have never heard a left-wing person compliment another by calling them “woke”.

If a friend of mine called me woke for voting in favor of trans kids, I’d ask if they were being sarcastic.

The more common usage in my part of the USA is pejorative.

It carries a negative connotation and refers to people who moral grandstand without an understanding of the subject matter. “Woke” people act as a moral authority on issues they are more passionate about than educated.

The best example I can use as a Latino is “Latinx”. We didn’t ask for that term, want that term, or use that term. Those outside the demographic that are pushing it against the wishes of 95% of Latinos are classic example of being “woke”

The positive side of that is what you’re describing. We call that empathy where you call it woke. Tbh this is also the first I’ve heard it described as a genuine compliment.
gpt
I think I read somewhere that it originated as black American slang for being conscious of various iniquities, repression, and so on. So some of the earlier pejorative users of the term were basically mocking black people, if I understand correctly.