As an example I think people from the American political left to somewhere(?) in the middle see it as what it has been introduced as, that being looking past the status quo and instead looking at your own values, i.e. the morality of homelessness and not having a disdain for them but empathy for them instead.
and then on the other side it feels like the people on the American political right see it as what this website describes it as “ A self-righteously moralistic person who behaves as if superior to others.”
I think the divide has originated from taking unlikeable behaviour and labeling that as ‘woke’ (in bad faith of course) and some people have just bonded to that definition so much that they see it as that.
At least that’s what I’ve noticed online over the past few (bonkers) years
People scoff and think of course I know what woke means, because the people the people they talk to/media they consume have the word at roughly the same level of meaning, not internalising the next more or less extreme group that isn't in their social circle include more or less in the meaning.
These days the word woke might as well serve the same purpose as "If by scotsman..." in that no one will disagree with you unless you get into specifics.