“Not everybody believes that there is a creator or a god.”
You are 100% correct. We have the free will to believe or not believe in God.
But that still doesn’t negate the fact that people are born either XX or XY, aside from rare exceptions otherwise.
These are some of the most common physical / biological examples. With known examples like these, I think it's possible that some people can have brains that are wired for the opposite gender, or are not completely wired male/female. We just can't confirm what's is in really in someone's mind yet (maybe a good thing considering possible government misuse). But it doesn't make these people liars, or mean that they should just shut up and suffer in silence.
http://en.wikipedia.org/wiki/Intersex
Intersexuality is the state of a living thing of a gonochoristic species whose sex chromosomes, genitalia, and/or secondary sex characteristics are determined to be neither exclusively male nor female. An organism with intersex may have biological characteristics of both the male and female sexes...
http://en.wikipedia.org/wiki/Klinefelter_syndrome
Klinefelter's syndrome, 47,XXY or XXY syndrome is a condition caused by a chromosome aneuploidy. Affected individuals have at least two X chromosomes and at least one Y chromosomes...
http://en.wikipedia.org/wiki/Androgen_insensitivity_syndrome
Androgen insensitivity syndrome (AIS), also referred to as androgen resistance syndrome, is a set of disorders of sexual differentiation caused by mutations of the gene encoding the androgen receptor... A person with complete androgen insensitivity syndrome (CAIS) has a female external appearance despite a 46XY karyotype and undescended testes, a condition termed "testicular feminization" in the past.