Yes, you can actually. These sort of arguments remind me of the transgender bathroom fears: What's stopping a man from pretending to be transgender in order to enter the woman's bathroom?
Well, the answer is that people that are transgender will have a history of being transgender or acting in such a way that confirms they consider themselves that gender. So any lawsuit as a result of this would look into your past, see that you lied about being transgender and make it an open and shut case. If that case became public then you could say goodbye to your job prospects.