I don't give a flying fig who (of any gender ID) uses the same bathroom as me as long as I can do what I need to do and leave without incident. My preference is to use the ladies' just because it is the "correct" one for the true me, but I would have no problem using a multi-stall unisex bathroom like the ones I've heard exist in some parts of some other countries as long as it was safe for me to do so. My biggest concern is "will somebody try to beat me to death against the sink if I use this bathroom?" If so, I evaluate my other options and choose the one involving the least risk to my health.
Of course, my clubbing days are behind me and, except for my current and hopefully soon to be former job, I generally don't have reason to go to the places where I am most likely to be at risk in the first place.