I just find the statement in the image really weird on so many levels.
Firstly the use of the words "trans person" as if there's just as much distress about sharing a room with a transman as a transwoman and for the same reasons.
A transman is biologically female and is not a threat in terms of risk of sexual violence. Of course among all the women who get hospitalised there will be some who are unpleasnt to be with but a transman has no greater or lesser probability of being any kind of problem so it would be irrational to care. They may be somewhat masculine in appearance of they have been taking testosterone but they are still fine in a female single sex room.
A transwoman is biologically male and is should not be considered to be any less of a threat than any other unknown male - obviously the vast majority of men are totally lovely people who would never do any harm and I am sure the same is true of transwomen but we have no way of knowning on-sight who is in the "safe" majority and who is dangerous to be with and it's stupid to be in a vulnerable state with any unknown man when you can't tell which category they are in.
So there is a rational logic for disputing the safety of a woman being expected to share with a transwoman.
There is absolutely no rational logic to dispute the safety of anyone sharing with a tory. They may be totally unable to grasp that the poor and disabled are not poor and disabled out of their own choice or moral defect, and have a totally unrealistic idea of what someone ought to be able to achieve if they just put in a bit of effort, but that doesn't make them a threat.
It's just a totally weird sentiment which seems to imply that anyone saying "I don't feel safe sharing a room with xxxx" is exactly the same as saying "I hate and despise xxxx" which shows such startling lack of intelligence and empathy that it suggests they cannot be a very good nurse.