I answered your question, as did several others. It is very surprising that someone with such a genuine desire for answers, and a superior grasp of English, missed them all.
But I'll answer again. Transmen are women, so by default they can use the ladies', and they can't use the gents', as men have sex based rights too. However, if a transman has modified her body so much that she really, truly passes as a man (very few do), then she can legally be excluded from women's spaces because she would cause the same distress and self exclusion that actual men would cause. It's also acceptable for safeguards to occasionally catch the wrong person. In fact they very often do, usually far more frequently than in the case of passing transmen. We generally accept it when we can't do X or Y for safeguarding reasons and I don't know why so many people think this shouldn't apply when men want in on women's spaces.
This does pose a problem to passing transmen but that's their problem; they chose to make such modifications that they no longer resemble women. Their doctors should discuss this with them before they make these changes.
So there is the answer to your question. You're welcome.