This is a man who has publicly gone out of his way to destroy a woman trying to do her job. That woman went to work on that day never expecting to have to deal with this and I'll bet as a result of his behaviour in refusing to go to the obvious unisex changing faculty, she is probably getting all sorts of threats, worries about her job, her own future.
It's always the same narrative in cases like this, where somebody who hasn't been able to get their way over somebody serving them goes to their manager and effectively says "I don't want them to get into A LOT of trouble (because I'm such a wonderfully reasonable person), but I DO want them to be clearly reprimanded and publicly humiliated, to prove that I was right."
The employee didn't make a single mistake and executed her job perfectly: somebody asked for a key to the changing room and she gave an appropriate one - there being two appropriate changing rooms for everybody of either sex (notwithstanding additional needs for those with disabilities).
In fact, she should be commended for her initiative and diplomacy, in seeing that the male making the request was dressed as a woman, and so guessing that he would probably feel more comfortable not instantly being given the key for the men's changing room, but would rather feel happier in the unisex room.
Lots of people would be perfectly fine in the unisex room; plenty of others would prefer to use the room exclusively for their own sex; exactly what innocent reason could there possibly be for somebody to be arrogantly expecting - and complaining as a result of being 'denied' - to be granted access to the one room out of three which is manifestly not appropriate for them? If Anne doesn't consider the unisex room to be good enough for Anne, then exactly who does Anne expect to ever be using that facility?