Well yes there would because communication is necessary and important. They may want to communicate this distinction outwardly in a way that can’t be ignored, in order to fight perceptions.

I do think your argument holds some water, that it can reinforce sexism to think rigidly in that way. But I think the leap from that to the conclusion misses the key context of the society and culture in which we exist.

And moreso the signals members of it use in order to find others like them, signal support, or signal opposition.