Oh dear I think you're confused.
It is mostly vulnerable women who are harmed by the removal of single sex spaces.
It is gender ideology that is the privileged belief which is why it is an phenomenon found mostly in the Western/ Developed world.
Notice how women/ girls in the developing world can't use gender to opt into the benefits of being male such as education. I wonder why that might be? But then even here the rules of primogeniture can't be circumvented by a woman identifying as a trans man.
One might consider this to be men's rights activism, if you really think about it.
Women don't get stand to gain, we lose words and rights in favour of males. There is literally nothing in it for women. Not one thing. Yet we shouldn't even talk about it.