My DH is involved in Women's sports.
I asked what would happen in men turned up and said they identified as women
It's already happening in sports.
Depressing, given that on one hand we laud films like Battle of the Sexes (Billie Jean King's story) but on the other in the arena of non-competitive sport, Swim England has issued guidance that:
^Some swimmers who were born female but now identify
differently may wear what is called a ‘binder’ – this is a
tight piece of material that is wrapped around the top half
of the body in order to compress breasts to conceal them
behind clothing. This is perfectly safe to swim in, and
should be encouraged.^
^Some swimmers may have a preference to wear less
clothing than usually expected. For example, some
swimmers may not want to wear anything on their top half,
so as to identify with their new gender, but if they have
not had top surgery this means that this person’s breasts
will be clearly visible. This needs to be talked about and an
amicable solution found. This may be appropriate to allow
during a trans specific session, but if a trans swimmer is
attending any other session in the timetable, then they
should be appropriately covered up – you wouldn’t allow a
woman to swim topless in a public session, and you need
to treat everyone the same.^
FtM trans are "encouraged" to cover up their breasts, and "not appropriately covered" if presenting as their new gender with no accommodation to how a "woman" might swim in a public session.
The double standards are rife. In professional sports it is a hot topic, and controversial.