I think a little more detail is needed. If the man was presenting as mail, I would say pull the other one. But if they were presenting as female, that is another matter. However, if she is transitioning, I would expect a paper chase of some sort. Some places even require a doctors note stating that it is unlikely that they will be able to function as a male due to HRT or something like that.
However, the solution is simple and actually makes better use of the buildings space. Rather than two changing rooms, you have one changing room with cubicles, just like most modern swimming pools have.