well its a difficult terminology to use because the right/conservative people are of course also against sjw/woke ideology. The distinction is that I'm criticizing very specific tendencies of some people whom could be best described as woke, not the underlying ideology. Such as when they weaponize privilege, language, race or sexuality in order to achieve some secondary unrelated or overarching goal. It's "the ends justify all means" mentality, if by democratic process you won't achieve consensus that agrees with your personal particular set of beliefs, then the rejection, destruction and undermining of collective decision making processes is justified. Which ignores the original reasons for why democratic structures exist in the first place (such as term limits and adversarial structures vs. corruption and abuse of power). This is essentially my criticism of some woke people.
It is very difficult to use the terminology even though it is the most accurate, because conservatives are the most loud adversaries of it, but they are just hateful racists, bigots, ableists, sexists, transphobes, homophobes, islamophobes, xenophobes, etc. Which of course invalidates everything they ever say.