The debate upthread made me think a bit, about how much easier this would all be if it was covered by criminal law.
The argument is not strong for S158/9 or Schedules 9, 12, and 16, because nobody was ever put in physical danger by decisions made about things like public boards, college fellowships, exceptional admissions to single-sex colleges, and clubs and associations. The civil law is enough.
But the Schedule 3 single-sex exemption exists to mitigate physical danger as much as to enable fairness and privacy. So should service providers be criminally liable, if they provide a service that relies on the exemption, but do not ensure that it is single-sex?
An example would be admitting a transman to an all-male ward, or a transwoman to a domestic violence refuge. ETA or a gym changing room, of course.