Your claim: "lavatories have "always" been shared by both men and women in Japan" now shifts to "Are you telling me that you have never been anywhere..."
That in itself is a dishonest shift.
That said... no. I don't think I have been anywhere where toilets are shared outside of some small cafes and restaurants where there might be a single toilet for use of customers.
There may be some incredibly rare rural onsen which are "konyoku" - i.e males and females bathe together, but these are not seen very often at all.
Otherwise, public places such as schools, universities, municipal gyms and swimming pools, parks, hospitals, supermarkets, zoos, etc... are all segregated.
Perhaps the only thing that might surprise a Western visitor is when men using the gents walk in and find a little old lady mopping the floor.
If you have better evidence than sheer incredulity then maybe you can post it. Otherwise, I have to wonder where you are getting your information from.