As a woman, if I am expected to share a changing room with a transwoman (who possesses male genitalia) why shouldn't I also accept sharing said space with a man?
You are asking me to accept on trust that inside the head of one is a female mind, but inside the other is a male mind.
Bollocks.
The answer lies in providing cubicles / sports for a third category "trans".
I don't think transwomen are any more likely to be predatory than any other person but I don't want to see adult male genitalia if I'm getting changed.
As a side note, women are already expected to share these spaces with children, including boys, disabled men and women and baby change facilities in many places.