Why should anyone have the "right" to perform intimate procedures on you? Care should be patient centred.
Regardless, single sex spaces and provisions are set up to safeguard against structural & physical inequalities between males and females, to the benefit of females because males are the oppressing class.
Racism, (or apartheid as TRAs like to bring that up too) exists to reinforce structural inequalities between black people and white people, to the benefit of white people.
In the racism analogy, it is not difficult to see that males (inc transwomen) are the white people, and females (inc transmen) are the black people.
That TRAs keep bringing race in to support their argument is racist and smacks of colonialism. Why should black people's struggle be used to support an ideology that ultimately hurts black women most of all (think of USA where black women are most likely to be incarcerated alongside males and lose sports scholarships to males).
That TRAs fail to see how back to front & illogical their argument is just shows how a fervent belief in something demonstrably untrue leads to a complete denial of reality.
NB mods & monitors - by TRA I don't mean "trans person". In my experience TRAs are most often not actually trans.
Also LTB