Creationists and social conservatives in the U.S. have created a bit of a cottage industry of making ridiculous claims about the effects of gay marriage - and other outcomes of secular morality that they don't like. Most recently, everyone's favorite creationist Ken Ham says that if we stop accepting the Bible as fact, this will lead to people not wearing clothes anymore. Compare to previous claims about gay marriage making people marry their dogs or legalize pedophilia.
It's very important not to be distracted by the individual issues where the social cons insist you listen to them. These claims (about gay marriage, teaching evolution, etc.) are distracting symptoms of a much more important central process, so my advice to fellow rationalists is that we shouldn't waste our time wading into the details of these sideshow debates, but rather confront them on their central complaint (which I'll get to in a second.) But the complete lack of interest in the actual outcomes is a huge hint. If you look at the way these claims come up in discussion with social cons, you can tell they're not at all central. I'm pretty sure Ken Ham didn't call conservative talk radio stations and say "Hey, I need some airtime so I can tell everyone about how lack of Biblical literalism will lead to mass nudity." Another great example: in 2009, a reporter challenged social conservatives to make concrete predictions about what would happen when gay marriage was legalized. None of them except one were able to tell us how the world would end. (As for the one that did, here we are six years later, and you can check out how well she did for yourself. Amazing! Many of these people were fighting against gay marriage as their full-time jobs, and they're not interested in telling us about the coming evils that they otherwise seem so invested in fighting.
Are they just dumbasses? Or do are they just not saying what's really motivating all of their whining? What's going on is all of their anger - against evolution, against gay marriage, against birth control and the right to choose - is really one big fear of theirs, taking different forms. It's not about evidence, you goofs! That's why when a rationalist argues with a theist about these things with evidence relevant to that particular disagreement, you're playing chess against a football team. It's not even about the outcomes of these things, or at least not the ones the social conservatives are willing to say out loud. That's why, when you can get these people to actually say what they think is going to happen (which is rare!), they quickly mutter something weird about bestiality or nudity (or something outright false and easily disproven), and then go back to complaining about how terrible it is that people won't listen to them anymore - which is actually what they're worried about.
What Ken Ham, and all the rest of them, really should say is "If you doubt my authority, and the authority of others like me, on matters of our origins or on sexual morality, then I will lose further control over people's behavior." That's it. This is how those who argue from authority behave when they're finally dragged out into daylight. And if these discussions run in circles, it's because their foundation for morality is "What's good is what Ken Ham says is good." But they can't say that out loud and expect people to take them seriously. So when pressed they flail apocalyptically and say "bestiality! Nudity! Et cetera!" (That said, Ham is more pin-downable than most, and he even uses the phrase "absolute authority" at the end of this bit.)
So let's try this: instead of giving someone statistics about how kids in same-sex households do, ask social conservatives "You have trouble saying what the bad outcome is that you're so worried about. This is really just about you trying to control people's behavior." Of course they'll sputter and object, and then you can ask them how a Muslim trying to do the same thing would act any differently from them.
*Note: for some time until a few years ago in that den of sin San Francisco, it was not in fact illegal to be naked, or at least not enforced. There were a handful (less than 10 in the whole city) of people who regularly took advantage of this. Somehow it didn't blow up into mass nudity. Interesting experiment, and relevant to this argument.
**As usual, there is a whole non-Christian world out there which is neglected in Ham's particular monologue. Somehow billions of people figured out clothing and marriage without the Bible.