I've argued on here a few years ago that apologetically insisting "I was born this way" (i.e. "I can't help it!") is no basis for arguing for one's right to live as one pleases, regardless of others' religious hangups, but it's taken the recent statements by Cynthia Nixon to bring the issue to the fore where it belongs. As Frank Bruni points out, no such argument from genetics has ever been required to justify freedom to worship as one pleases, and yet this is a principle which is universally* accepted in the Western world today. Why then should a "born this way" argument be necessary for gay rights?
On the other hand, just because an aspect of a person is accepted as being genetic in origin doesn't mean prejudice automatically goes away, as the black experience testifies: on the contrary, 4 centuries of slavery, segregation and discrimination in all aspects of life have actually been justified on the basis of the supposedly innate - and therefore irremediable - inferiority of people of African descent. Similarly, more than 1000 years of European antisemitism wasn't helped in the least by the reclassification of Jewishness as an "innate" attribute in 20th century Germany; again, the conclusion drawn was that being Jewish was a congenital flaw which would only taint and undermine German health without the taking of strong measures ....
Finally, I think it's worth noting that the "born this way" rhetoric, apart from being cravenly apologetic in implying that those who make it would indeed be willing to change their sexual orientation if they could, doesn't even make sense on its own terms. Just because a trait is unchangeable doesn't mean it's congenital (just ask Heather Mills), while there are many congenital traits which can indeed be rectified through treatment (e.g. astigmatism). The real issue shouldn't be whether homosexuality is due to nature or nurture, but why anyone should even have a say in whether or not others chose it. I say that what others get up to in private is neither my business nor the government's, as long as no one is being forced into anything.
I can certainly appreciate that many gay people will find Cynthia Nixon's statements absurd: I personally can't imagine any circumstances under which I could be persuaded to give up women for men, so it's easy enough for me to see why someone of a different orientation would feel the same way I do. That Nixon's statements don't apply to me doesn't mean that the actress' words have no validity for her, however, and in any case her personal experiences should have no real bearing on what is in reality a matter of individual liberty in the face of religious tyranny.
*The likes of Hungary excepted.