The role includes "sex-based" labels and "sex-based" segregation.
These are parts of the role, which you militantly uphold.
This gets to the nub of it.
Single-sex sports for women, single-sex prisons for women, single-sex rape crisis centres for women may be "role play" for you, but I can assure you for women they are a necessity.
This is the paradox - we've reached the progressive point that on the whole most of the "role" part of the sexes had been eliminated, leaving sex segregation only where truly necessary.
But now those who are desperate for there to be a role play have to try to get themselves into those necessary areas for validation.
And their egos and entitlement are so high they're not even prepared to accept the previous status quo, which was that a very select few men might be permitted into this sort of "witness protection programme" with careful screening and gatekeeping - no, they're insisting that any male be able to enter these spaces on demand. That was never going to fly.