I’d wager that a big reason the religious right is so adamant that allowing gay marriage will bring about the destruction of society (such as Kirk Cameron claims) is that if gay marriage becomes legal everywhere and civilization doesn’t collapse, it will undermine their authority to the point of tearing it down entirely.
So really, it’s not that they necessarily believe on a rational basis that these things will happen so much as they insist that it has to be that way, because otherwise their faith will be shaken. Such is the difference between science and religious doctrine.
Which is, again, why I have never cared if someone thinks gay marriage is wrong on a personal level. That’s your right. Hell I don’t even care if, as Patton Oswalt notes, your reason is just that you think gays are gross. But it’s when you think it has to be kept illegal for the “good of society” that I now have big problems with you.