When a trans woman uses the lady's room there is no man in the lady's room. When a trans male uses the lady's room there is a man in the lady's room. Now you are saying a man used the lady's room then there was a man in the lady's room and he should have been dealt with as such. I have been using the lady's room for 8 years and with most of them being one seaters or two stalls. There is little differences from the men's room except for a place to put lady's hygienic pads for their periods. There is no problem.
Now when it comes to dressing rooms for swimming pools, gyms, and PE classes in schools, I have never dealt with that because at 69 these are not an issue for me because I never go to these places. The ocean is a wide open place with no dressing rooms and I just wear a one-piece.
Most trans women are not interested in having anyone seeing their private parts, especially when they have not had surgery in those spots yet. I would have a bigger problem because my breasts are just wearing two padded bras and in the dressing rooms, it would be obvious that I do not have breasts yet. If I need to, I would just use the ladies room to enter the gym or the pool and take care of showering and changing at home.
But since a trans woman who identifies as a woman would never be a man in the lady's restroom or dressing room. Each person finds a way to keep their private parts private. Go to a gym that protects your privacy. Swimming pools you could just wear your swimming suit under a pool dress, then get out take your shower in your swimming suit and put on your pool dress and leave. In the gym, just wear sweats and shower and dress at home.