What they were saying is that if you accept that a person is a girl because he or she says they're a girl, it's only fair to accept Lizard Man as a lizard because he says he's one.
Well, that's a terribly analogy because SEX is biologically determined; GENDER is a social construct.
But setting that aside, if some dude tells me that he's a lizard, then he's a lizard. IDGAF.