What about going to the bathroom and dressing in public places where - gasp! - lesbian women are allowed to go?  I mean, trans women are women and like men.  Whereas lesbian women like women. Then there are your bisexuals and a whole lot more people that look to be female or male, but...
Do you have any idea how ridiculous you're being?  If you're that concerned about personal privacy, dress at home or carry a portable privacy curtain.  As for going to the bathroom: make sure the toilet door is locked.