I don’t mind when women come into the men’s room. Sometimes they have to because the women’s line is just so darn long. I’ve taken my woman in there several times at concerts and sporting events. Never a problem and normal men are cool with it.
I think the answer lies in providing individual, private stalls or rooms. Modern stores need to be retrofitted with this accommodation. Like Starbucks (I know, ugh) has individual restrooms that anyone can use. Everyone is alone in there, so who cares?
Some large events have a bank of stalls, with hand washing available outside for everyone. Works fine.
The typical restroom with multiple stalls/urinals is a relic of the past, thanks to the “trans”gendered. In order for everyone to be safe we need individual, private, locking stalls available for males and females (and others smh).