Don't know what country you're in. If you're in the US, your employer has a legal obligation to provide you a workplace that is free of harassment. If your treatment rises to the level of harassment and is based on your gender presentation or identity, that is considered sex discrimination by the EEOC. Your employer is required to address the situation and not simply say "ignore it".
My advice (though I'm not a lawyer):
* Write everything down. Document everything your coworker or your employer says, with times and dates.
* If you're a member of a union, consult your union. If not, look around for a local LGBT rights agency, like Lambda Legal. Most areas have them.
* Before you quit, speak to your employer. Be very professional, but tell them you are being subject to a hostile workplace and ask that they do something about it.
Good luck. You have a right not to be treated badly at work.