A woman with Swyer Syndrome and 46xy (male) chromosomes could get married to a woman in Kansas (by Kantaras vs Kantaras, male chromosomes == male), then move to Louisiana, and marry a man. Neither state would recognise the other marriage as valid, so there's no question of bigamy. Things would get very complicated if she became a surrogate mother, from an egg donated by her wife and fertilised by her husband.As she well might.
I remind everyone that I have dual UK/Australian citizenship. Were I not married (to a woman), here in Australia I could only marry a man (as same-sex marriage is forbidden), and in the UK I could only marry another woman, again as same-sex marriage is forbidden. Different definitions, again.