I think a large part of the problem is that abuse or overuse of a term often renders it malleable to a point of meaninglessness in many situations.
When someone decries the "woke" in a context where they don't elaborate on what they mean, the backdrop that imbues the term with meaning is not there in the first place, so the implications of the word could pretty much only be guessed at unless there's more context.
I have seen some people denounce others as "woke" or "radical" merely for opposing mass slaughter of their people and friends. No, I'm not exaggerating; without knowing much of anything about the latter, the former used such terms to dismiss the vast array of concerns with a broad brush. Is it any wonder that some who experience such egregious dismissiveness for supporting their people's very right to life would be wary upon seeing a weaponized or vague brandishing of malleable terms like "woke"? Using a term to summarily denounce and minimize other perspectives and those who hold them in lieu of trying to understand others seems to me a far cry from good-faith discourse.
Not that I think the term can't ever be used reasonably, whether in an approving or critical context, but I just avoid it altogether because it has become, in my opinion, too malleable, weaponized, and enmeshed with political extremism from different camps.