I think the conservative groups are right that having society OK homosexuality is likely to lead to society's eventually OKing polygamy. At the moment I'm not convinced that OKing polygamy would necessarily lead to problems.
I think you may be able to draw a good analogy with money: imagine you're in a society where everyone can only make a certain amount of money per year (say, $50,000). Everyone makes the same wage/salary, although you have the option to quit your job and not make anything. Would it cause society to fall apart if you made it OK for some people to earn more money than others? Most societies in the world have a system-of-inequality like that and it seems to be working out fairly well.
In addition, keep in mind that even so-called conservative-values guys like Rush Limbaugh and Newt Gingrich have gone through multiple wives; it seems to me that's basically polygamy.
2010.10.19 - WIRED - How Beer, Oprah and Sergey Brin Can Help Cure Aging
It’s public knowledge I am polyamorous as well. That’s something that goes down not so well with some of my more politically sensitive friends and colleagues. But it goes quite well with some other people. [laughs]
(...)
We’ve got obviously a much greater incidence of serial careers and relationships, just because people are living longer and having more opportunity to do different things in their lives. That definitely seems to be something that’s going to naturally extend.
And in relationships, well, I just told you I’m pretty adventurous that way. That’s actually something I feel quite strongly about. The whole monogamy jealousy thing is a bit archaic, really. [laughs] It probably won’t last very long.
2015.06.26 - Politico - It’s Time to Legalize Polygamy