You're absolutely right that there's a right-wing archetype that wishes to leave the term "woke" intentionally amorphous and open-ended so they can weaponize it as a go-to invective.

But there's also a left-wing misappropriation of the term, which is why I distinguish "woke" (caring about social justice) from "hyperwoke" (virtue-signaling, performative allyship, and savior complex). I write more about it here:

https://medium.com/the-bad-influence/yes-i-will-keep-using-hyperwoke-as-a-pejorative-a2b47ac8d4a7