I think the amorphous nature of the Right's usage of the word "woke" is the problem. Conservatives and moderates definitely have identified a very real problem when they call out "wokeness" -- but it needs to be narrowly defined in a much more intellectually honest way.
The problem is that the Left has its own illiberal version of "woke-shaming" that THEY try to weaponize against anyone who doesn't believe what they believe in. This is why I make the distinction of calling it "hyperwoke" (rather than just "woke" by itself), while offering an intellectual explanation for what we (Independents) are railing against:
https://medium.com/the-bad-influence/yes-i-will-keep-using-hyperwoke-as-a-pejorative-a2b47ac8d4a7