What quantifiable characteristic does a transwoman have, that is the same as a biological, natal woman?
Think about why natal women need, and originally campaigned for single sex spaces. To escape from male threat and control.
Unless you define a woman as how someone dresses, and their internal feelings about themselves, a transwoman is a man. The clue is in the name. Trans means opposite.
And, even if you, personally, chose to define women as a state of mind and clothes, many of us don't.
I'm a woman, to every last cell in my body. There are situations when biological sex shouldnt matter, but when the situation involves removing clothing, consent matters.
I don't consent to getting changed in the same space as a male, regardless of how nice he is, or how he feels or 'presents'.
Are you going to force me?