Trans people existed 50 years ago, and they used the bathrooms they identified with, not the sex they were born with. People just talked about it less back then. There was less visibility. Sometimes they called it something else, trans sexual was used a lot. What we call now gender affirming surgery was called sexual reassignment surgery.

Here are some examples:

Christine Jorgensen

https://en.m.wikipedia.org/wiki/Christine_Jorgensen

Lou Sullivan

https://en.m.wikipedia.org/wiki/Lou_Sullivan

Roberta Cowell

https://en.m.wikipedia.org/wiki/Transgender_history#:~:text=Accounts%20of%20transgender%20people%20(including,in%20the%201950s%20and%201960s.

A trans gender person is someone who identities as a with a gender that is different than their biological sex.

A woman is an adult human female, or an adult human male who identifies as a trans woman (see above definition).