That is why it is necessary to ask whenever a rule change is made is how incentives will be created for people to follow the rules to maximize their personal benefit. For example, changing gender to get lower insurance rates is a perfectly rational use of the rules yet it was not intended. Changing gender to get access to places for sexual gratification is another. At some point the potential for abuse is so large that some limits have to be put in place even if that means creating barriers for people who legitimately needed the rule change.
Perhaps we should just not allow insurance companies to charge rates based on gender, as they have done in the EU. That way, a 'barrier' is created that will prevent men from changing their gender on paper to gain cheaper insurance rates, and it won't create barriers for those who really do need a rule change. Perhaps in the other situations under discussion there are also changes that can be made to the system to prevent abuse of rules, rather than the people who legitimately need and benefit from those rules. I'm not sure what changes might work, but I am coming to agree that submitting mere paperwork to change one's gender on government-issued ID is a bit lax; perhaps a demonstrated commitment to the 'other gender' identity needs to also be proven, and that this commitment must have been apparent for a significant length of time. Not that someone won't game that, too, at some point.
Of course, those born intersex and 'assigned' a sex at birth shouldn't have to go through the same onerous procedure given that it was the decision of someone else to impose a visual sexual identity. Paperwork demonstrating the sex assignment at birth should be available and acceptable for those people to quickly change the gender on government issued ID. And again, no doubt someone will concoct a way to game that, as well.
Thinking out of the box a bit, perhaps at age 21, all adults should be subjected to a test that determines what arouses them: naked men, naked women, naked children. This information could be included in government issued ID, and that could be used to determine access to public places where nudity may occur.
Or, perhaps we could simply change the morality within our society, so that 'nudity' becomes commonplace and not assumed to be a signal of sexual availability or interest.