As I've said many times, if you don't like a hostel being trans inclusive then take it up with the hostel management, don't attack a resident who quite possibly has little choice but to be there. And if you think trans inclusive shelters should be banned, despite mixed sex ones being legal, then say so, but perhaps drop the allegation that it's trans people who are the authoritarians.
By communal bathroom I assume you mean a private bathroom, shared by different people, as you might find in any flat share which would be the arrangement in most hostels. You are certainly making a lot of assumtions. How do you know their facebook page was public, given how fast facebook removes public photos of that nature it seems unlikely tbh, the pics and screenshots could well have been leaked. Do you even know if that photo was taken in the bathroom of the shelter, people have facebook pics going back years?
The tweet clearly reveals she is somewhat surprised by morning erections returning after her hormone regime was changed. She could merely have been clumsily saying this made her feel a bit awkward going to the bathroom in the morning. There's no evidence anyone saw her, no evidence she exposed herself to anyone, and no evidence of a victim. If there were then I would hope the hostel staff did something about it, which could have included kicking her out or informing the police. But there's no evidence this happened.
Yes her tweets are a bit uncomfortable, but they weren't meant for us to read were they. And it is very common for people with mental health conditions or substance misusers to sometimes say inappropriate things. According to the shelter: "This low-barrier system accommodates women with severe mental health and addiction issues. Each night we shelter up to 150 women with beds for 57 women, many of whom have been rejected by other shelters. As the focus is harm-reduction, women will not be turned away."
I know of a couple of projects like this. They have impeccable safeguarding and security procedures. They will also deal with much more serious incidents than this on a regular basis. If you don't like that they allow trans women in take it up with them. Do not sexually harass and make lurid allegations about a vulnerable service user based on a couple of tweets that really tell us nothing at all. I would have hoped a professional in this kind of field would understand why that's a problem.