Emily's Cat
Rarely prone to hissy-fits
So - to address one of your negations above - which locker room (given a choice of "men" and "women") should a transwoman use when she visits her local municipal sports centre?
(Or, of course, which locker room should a transman use in the same circumstances?)
Use the one that other people are most likely to assume they belong in.
Have some self-awareness and use a mirror. If you look mostly like a dude in a dress, use the gents. If you look mostly like a chick in jeans, use the ladies.