Maybe I am wrong, but as someone who identifies as right of centre I don't see any of this as woke.
The word woke gets my goat as it is just a right wing way of trying to keep the equilibrium of fat rich white guys trying to run the world.
Thursday morning soap box now put away.
It's been turned around to mean the opposite, similar to "do gooder" as an insult. I accept that language changes all the time but (although I have at times) I try not to use this type of manufactured word to suit an agenda (cis, terf, transphobic etc). The original meaning has long gone, much to the annoyance of the woke oops I said it again.
There is a convenience about it though, as in it's an easy way to describe a group of self righteous people without having to list everyone of their sanctimonious traits.