[smudgie]

I just can’t see a problem here.
Firstly, mixed wards are or were the norm, but I have never seen mixed sexes/genders allocated to the same room.
The only time the men and women would meet was in the day room or the corridors.
I have absolutely no problem being admitted to a mixed ward, just as long as they have enough privacy available to all.
As an older person, I would have no issues with sharing a room with a trans person, more concerned about anyone snoring and keeping me awake.