Separate washrooms are simply more practical for multiple reasons.
Did someone catch a glimpse of a wiener as they finished at the urinal? Is that sexual assault or indecent exposure? Imagine the notion that someone could point, scream and ruin your life, just because you need to pee.
Who's to say what happened?
That's just one of many reasons that washrooms should be separate.
The flip side is that you don't want perverts in washrooms trying to catch a glimpse of anything.
Was that happening or was someone just walking past a stall and happened to look sideways?
Again, who's to say what happened?
The only people who would benefit from it is lawyers.
It all comes down to 'intent' and who can know that when everyone is free to be in either place?
You know an easy way to prevent such "misunderstandings"? To have areas where it's know that other groups should not be going into that zone. If a man is in the girls washroom then there's something wrong simply by virtue that he's in there, likewise a man doesn't need to worry about being accused of anything by a girl as they shouldn't be in the mens washroom in the first place.
Basic. Common. Sense.
Oh, and too many "transgender" people are either mentally unstable or use it as an excuse to be abusive and / or get away with being a pervert.