When you say "No, anti-woke doesn't mean anti- Black! It also means [things that aren't Black] too!" that's like saying "No, anti-Shabat Shalom isn't anti-semitism! They hate [group that isn't Jewish] too!"
Because woke means Black. Woke is a Black saying. Saying that you are anti-woke means that you are anti-Black.
And racists and Nazis hate Black people, Jewish people, women, LGBTQIA people, and many other marginalized groups. Racist men do not care about your reproductive rights.