Gender is a social construction, so why not.
Sex, there's male and female generally speaking in the animal kingdom, barring a few exceptions.
eg This person (and many like her) was born physically a male, but through surgery and chemical therapy(after psychological evaluations), they've become female, to better fit the gender they identify with more closely.
If some people want to argue she's still a man, despite how her psychological make-up works and what her body has gone through, they're probably retarded; at least on some level. Funny thing, must of the guys who would say she's a man wouldn't know she was born a male and would probably have sex with her never knowing.
If she used a men's restroom as she's supposed to according to these people, it would raise eyebrows.