I think it's okay to refer to the word "woke", but if you use it more than 3 times in your writing, then it's hard to take you seriously.
Why?
Because it's a word that gets people emotional. Getting people emotional is the opposite of what you want to do when you're trying to intellectually dissect something. But it's exactly what you want to do when you're grinding a gear.
It's just like if somebody wrote a piece about trump, but mentioned he was a felon 4+ times, you'd know they weren't writing an unemotional thinkpiece.
