If you have a good sense of humor, you CAN'T be truly "woke". 😁
By my definition, there is a big difference between being "woke", and working against racism, sexism, & other kinds of oppression. Being the latter is simply being a good human being. But "woke" is morphing into just another poisonous brand of identity politics that seeks to normalize intolerance for other perspectives, extreme political correctness, and seeking things to be outraged about so one can virtue signal their "woke-ness". One might say the extremists have co-opted the "woke" identity. The push to 'cancel' J.K. Rowling and classifying her comments last year as "trans-phobic bigotry" (instead of just being a different perspective) is a perfect example...
So no, you are not "woke". You are just a good human being... 😇
It's just a word. People put their own meanings on it and turn it into an insult. Finding the line between humour and abuse be tricky. The intention and how it's taken can differ. There are those who will weaponise this, but they are the minority. The internet tends to amplify their voices. Fighting this sort of discrimination can be as important as dealing with actual hatred. It's all fun and games :)