I've read some of your other posts and found them mostly well-reasoned and persuasive, but I think the argumentation in this one needs work. It doesn't seem that you've directly addressed the core concern here, which is:

Is there a valuable protective role in being able to tell, in most cases, at a glance, whether or not someone belongs in a particular restroom?

You say a variety of things that sort of implicitly get at part of the answer, and would be great additions to a comprehensive answer, but it would be a lot more compelling to tackle it head-on.