It does happen. There are a bunch of cultures where your sex organs aren't determinative of your gender role. And there are cultures where they are, and people say fuck that and live a different gender role anyway. A fair number of European soldiers, sailors, doctors, and so forth were found to have an unexpected set of sex organs during autopsy. There have always and everywhere been people we would consider trans, and some cultures have and have had accepted social roles and gender roles for those people. And in cultures that haven't people transgressed against cultural norms when they could to try to live a more authentic life.