This is the main crux of the issue that they refuse to discuss: when TRAs proclaim 'trans rights are human rights', they are deliberately keeping their cards close to their chests.
What they are demanding is that, in addition to the human rights that they - and everybody else - thankfully already have, they should be allowed to take some of those rights from other people and then add them on to their own, so that they end up with more 'human' rights and others are left without some important ones of theirs.
If anybody disagrees with what I just said, look at Rose's main summary of the complaint which horrifies Rose so much: "So I would be segregated if I needed to be on a ward".
Yes. Yes, Rose. You and everybody else who is too old for the children's ward will be segregated, with the males put on the male ward and the females put on the female ward. Why do you assume without comment that it's perfectly fine for all of the other adults to be segregated strictly depending on a basic biological fact that nobody can change, but YOU should have the privilege to choose whichever one you fancy more, regardless of the reason why single-sex wards exist in the first place and completely disregarding what anybody else on those wards wants?
So we've established that trans people do indeed have the same human rights that everybody else has - which is, of course, a very good thing that nobody is trying to quibble. Our question, therefore, is why YOU are actively seeking to take human rights away from other humans? What kind of entrenched misogynistic and misanthropic gynophobia would make you even think to want to do that?
I think you would be as well to check your privilege and, if you really do care about justice for everybody, start campaigning on behalf of those who have less privilege than you do - including the vulnerable women who are being denied their right to protected single-sex wards and other personal/intimate facilities.