Not sure what your point is here. When the right speak of the woke, we refer to the people calling themselves woke and what they do. The definition can change not based on what conservatives say it is, but based on what people who follow it do with it.
Same thing with socialism - the left will walk under the banner of socialism, make changes based on socialism, but when it goes sour, they claim it wasn't socialism. Same with the term woke. When it was supposedly for equity, you loved the term, but when equity and other woke ideals led to violence and racial hatred, all of a sudden woke needs to be redefined. Same old game you play, and no one's fooled.
Movements aren't defined by results, they are defined by actions that lead to results. And as soon as people can get on board with that, we can have unity. Without it, we just have stupid discussions about terminology.