No you don't, but that is a false comparison anyway. The "accomodation" is simply superimposed on the psychiatric situation at hand. There is the reason the transwoman is there and then there is the logistical issue as to where to admit them.
But the general outrage at the notion of protecting women in a psychiatric emergency facility from a transgendered woman acting out in their crisis is quite telling. Compassionate and professional care aside, the requirement of any and all individuals, even in crisis, to a potentially harmful situation is a foregone conclusion. i.e. a biological male in crisis being housed with a biological female in crisis. It is an irrational and non-scientific decision to put the two together.