How is a fear for safety in a confined space for a weaker human irrational?
In that specific space as opposed to any other? Absolutely irrational,
especially since sex-segregated bathrooms are only a "suggestion" with no "enforcement". It's a cultural convention, and of course there's supposed to be a (presumably much stronger) cultural convention against sexual assault, too (not to mention penal sanctions), but that doesn't appear to bother sex offenders, so the presumption that a little sign on the door constitutes "objective safety" is, indeed, "irrational". It is an
extremely unfortunate fact of their lives that women do in fact,
quite rationally, have to bear in mind, to one degree another, the risk of sexual assault any time they're in public, but believing that maintaining sex-segregated public lavatories does anything real, much less significant, to obviate that risk is both ridiculous and, again, irrational.
(I know I said my last past would be my last, hopefully I'll be able to restrain myself from further comment, because this has gotten ridiculous.)