I don't believe that stating a man can't become a woman, isn't the same though!
Why?
Because ultimately in order to be professional you have to treat a male patient as if they are male and a female patient as female. You need to understand they may be on medication or have had surgery because of their trans status. Because if you don't, you are unprofessional and risking their actual health!!!
Stating 'I think transwomen are below contempt' in any sende would be unacceptable though. But that's fundamentally different.
And the post in the OP falls into this latter camp as a direct attack on a group.
Beyond that, arguably being on a single sex ward, could put them at risk because if they do 'pass' visually you get the risk of HCP not checking notes properly and treating them as the wrong sex.
In a private room, it does make it clearer that their is a need for caution about their sex and even pronouns. Which is actually better and gives more protections for this person whilst protecting their dignity too.
It's so much more appropriate for all concerned.
And it's nuts that staff are being disciplined for observing reality whereas those who state a belief which attacks non believers for their beliefs is able to stand and
a) isn't challenged
b) even in a sensible debate there is this notion that stating a man can't become a woman in the context of a medical setting is the same as a full on ad hominem attack on a group identity based on political beliefs.
One is stating the actual truth and highlighting actual practical issues
The other is just a political prejudice.
And the wrong one is being attacked as being unacceptable.