And it's funny you recognize the usage of "woke" as problematic, but you still use it. Actual liberal politics means schools, roads, health care, climate, etc. It means a social safety net and labour protections. All of that are universal in Europe while most of it is completely lacking, as I said in even the most "liberal" parts of the US.
Confusing policy (what matters) with social media arguments about what a woman is defined as is a distraction. It's meant to divide people that otherwise agree. Don't play into that game.