I think that 'woke' was originally meant to imply that someone was alert to social injustice (itself a very flexible and politicized term), especially in forms that may not be obvious. The potential for misusing the term and using it as a political weapon should be clear.
The problem with trying to use such malleable terminology is that it becomes easy for the word to be redefined so as to work against you. Now, a 'woke' person is one who is overly sensitive to what might offend others, and who has decided to be so on everyone else's account. And they also like to borrow the supposed grievances of others to use as a weapon, which ends up being an actual example of appropriation.
So, depending on which end of the political spectrum you are, it is either a badge or a label (or an albatross). I find it to be a meaningless term, pretty much from the beginning.