This was an issue at a place I worked. We had a gentleman who was transitioning to be a woman. As part of this he petitioned to be allowed to use the ladies room. He was about 6'3", built like a lumberjack, had a full beard, and dressed like every other guy there. But he said he felt more comfortable using the ladies room since he was in pre-op (taking hormones, going to classes, etc.). Needless to say we had a full on row over the whole thing. I let HR deal with it mostly. In the end we provided access to what was basically a single handicapped bathroom in the main offices for his/her use. It didn't make him/her happy but we had a contingent of women come to HR to complain and had to find a solution of some sort.
So he wasn't yet living as a woman, which I think makes all the difference in this discussion.