The idea of "gender identity" as based on a subjective inner sense of self, and that "gender identity" must supersede sex, fundamentally reframes a core characteristic of the entire human population.
When implemented in law and policy, this affects everyone.
The impact is mostly on women and girls, for whom female-only spaces are essential for their safety and dignity. Allowing any man who says he's a women into such spaces undermines the very reason they exist in the first place, and effectively destroys them.
This isn't progress; it harms women and girls. It shouldn't be a surprise why so many people are against such changes being imposed.