Basically, here is what exactly I am wondering about:

As far as I know, the Equal Rights Amendment (ERA) failed at least in part because conservatives such as Phyllis Schlafly argued that the ERA would have resulted in things such as the legalization of same-sex marriage nationwide (though that ultimately ended up happening even without the ERA!) and the abolition of sex-segregated restrooms and sex-segregated locker rooms nationwide. At the time that the ERA was seriously debated in the 1970s (and later as well), supporters of the ERA criticized Schlafly and other ERA opponents for making such arguments.

However, what I am wondering is this--were Schlafly and other ERA opponents correct in regards to this?

After all, symmetric discrimination is still discrimination. Indeed, do ERA supporters believe that a restaurant which (purely hypothetically) has "separate but equal" places for men and women to sit in has a seating policy which is unconstitutional? If so, why exactly shouldn't the ERA (if it will ever actually pass in the future, that is) be used to declare sex-segregated restrooms and sex-segregated locker rooms to be unconstitutional nationwide?

Basically, similar puritanical arguments which are used to justify sex-segregated restrooms and sex-segregated locker rooms can likewise be used to justify things such as "separate but equal" seating for men and women at restaurants, et cetera. Indeed, if that type of puritanical logic is rejected in regards to things such as restaurants, why exactly shouldn't that type of puritanical logic also be rejected in regards to things such as sex-segregated restrooms and sex-segregated locker rooms?

Anyway, any thoughts on everything that I wrote here?