The only real issue with "bathrooms" is that when men use a urinal, their dick is partly exposed, which gives some women cases of the vapors. I've heard that women could use a urinal, but I cannot and don't want to imagine how that could happen with anything other than a skirt.
But where it is really important is when you have thousands of people wanting to pee at the same time. Think rock concert or football game. With a wall of urinals, things move along at a good pace. If all you have is "stalls" to do your business, men will revolt. They will miss a significant part of the proceedings.
Women deal with all-stalls, and God bless them. I wouldn't be happy with that.
There is no such thing as trans. Either you have a dick or you don't. End of story.