"how do you ensure that the only people in the changing rooms are biological females?"
Decent law abiding people of both sexes will follow the law.
If a trans women or man ignores the law and enters a woman's only space....they/he can be reported and removed by security/police and dealt with by the law. Until they/he learns to obey the law.
What you are suggesting is that some trans women or men are not willing to obey the law. In which case that is an issue between the police and the trans women or men, nothing to do with women.
We would be safer, as we can report a man on the bathroom and know that only women should be present.
We don't cancel laws because people break them, we punish people to try and prevent repetition of crimes.
I don't think trans women would continue to use our spaces if companies/government strengthened our rights to privacy and dignity. I have faith that the majority of trans women would do the right thing and follow the law.