No, I don't think a Muslim woman's right trumps a transgender right. I don't think any kind of religious right should trample on any type of human right. If the law regards a transgender woman as a woman, she should have a right to exercise in a woman's facility. If that makes any Jew, Christian or Muslim, uncomfortable, that's too bad.
You're talking around the problem here. Rights don't 'trump' each other but they have to be resolved when in conflict. Religious rights already supersede human rights in several specific examples. It seems to me, reading this paragraph, that you may not realize that.