I don’t like the word “woke” because it is to grammar what fingernails are to a chalkboard. Also, I presume it comes from Black American slang, and while it’s indisputable that a tremendous number of standard American slang comes from different aspects of AA culture, this particular one seems too close to what could legitimately be claimed as “cultural appropriation.”
I can’t believe I’m about to type this, but: people who aren’t “people of color” can’t really be ‘woke’ to what people of color face. My daughter had a close friend who is from the Dominican Republic. He faces subtle and sometimes not-so-subtle discrimination regularly in the way people interact with him. It upsets him, he doesn’t fight back against it (because he can’t, really) and he expects it.