I honestly have no issue with anyone using any cubicle.
It's weird fixating on this everyone has their own cubicle. The only shared areas ore the hand washing. No idea how anyone can get worked up about that?
So here's why I 'fixate' on the issue of male bodied people in women's loos:
Many years ago, I went to a football match (West Ham v Wimbledon, was pretty shit). About 15 mins into the second half, I needed to go to the loo so set off down the basically empty corridors and into the completely empty women's loos.
As I went in to the washbasin area, I heard someone behind me and saw out of the corner of my eye that the mirror was showing a man a couple of steps behind me. This was the 90s (so lots more women with short hair than now) and everyone was wearing basically the same clothes in the same colours (much less gender colour coding with adult clothes back then) to a football match. The person behind me was dressed pretty much the same as me except for a baseball cap, so couldn't get a clear look at the face. But it was immediately obvious that it was a man, because of the body shape and the way he was walking.
The fact that I could instantly tell it was a man that had followed me into an empty women's loo was what saved me from something very nasty happening. I got into the first cubicle and bolted the door, just in time to stop him opening it. He started shaking the door. When that didn't work he pulled himself up on the side of the cubicle to look at me over the gap at the top; I can still see his stupid grinning face wedged between the cubicle top and the ceiling. All the time he was trying to get me to let him in.
Very luckily for me, he was obviously thick as mince as well as drunk and/or high, because after a while (fuck knows how long - felt like a long time), his mobile went and he stopped trying to break in and rape me so he could have a chat with his mate. I took the opportunity to get out as fast as I could (successfully).
If that had been a mixed sex (what the terminologically confused like to call gender neutral) loo, I wouldn't have known that anything was necessarily wrong - I might have wondered, but I wouldn't have known, and I wouldn't have had any reason to speed up and get into the cubicle as fast as I could. I'm pretty sure that loos being single sex are what stopped me from being raped.
So yeah, too right I fucking 'fixate' on women having single sex loos.