When conservatives use the word “woke”, they are using the same meaning as people on the left. The only difference is they think what the word describes as bad. That’s a difference in evaluation, not a difference in meaning. A person who says “I like dogs“ means the same thing by “dog“ as someone who says “I hate dogs“. You might want to claim the first person means “ adorable animal companions“ and the second person means “smelly creatures that slobber and bite people“, but that would be a mistake. Because they both agree on what the word means, these two people can actually have a conversation about their different evaluations of dogs.
I will continue to use the word “woke” in all of my writings on the subject, because that is the only word available that unambiguously refers to that subject. If you substitute some other word, eventually people you disagree with will start using that new word, which will thus be tainted and require you to change the word again, and soon ad infinitum”. That is what happened to the word “political correctness”,which is a synonym for woke as it is now being used. I wrote an article called the Woke revolution in moral habits about this important social movement, which tries to clarify its goals and suggest some new strategies. I’m not going to rename the article every two or three years because the name of this movement is being used by people who hate it.