Most of the problem TRA face is of their own doing, though.
They only things someone need to get a GRC is to have a diagnosis of gender dysphoria, two years worth of id and, at the time of its introduction, a divorce if married. He chose to have surgery, it isnt part of the process.
So for the rest of the population, the person hasn't changed. There is no sex change.
And the rest of the country need to have single sex spaces.
If they made the conditions of getting a GRC that the applicant was always percieved to be the opposite sex, the arguments that single sex spaces had to be single sex would be harder to argue. And those with GRC may have been included in the opposite sex spaces.
But TRA made it into a admin process only. Why would spaces be needed for women and men with documentation? How could they be justified?