The OP knows that gay marriage is a heated political issue. I think it's a fair inference that they know polygamy is, too. The OP brings up both, as well as the question of whether "polies [should] campaign for the right for a civil union."
I'm pretty sure that the OP is talking about polyamory, not polygamy (I don't know if you were unaware of that, or if you deliberately brought up polygamy as an analogy).
If I wanted to be cynical I'd say that polygamy and polyamory describe pretty much the same phenomenon, except that polygamy is detestable and reactionary and oppressive, whereas polyamory is the complete opposite; or that polyamory is when it's done by fashionable white people, and polygamy is when it's done by weird brown foreigners (I don't think either of these is a fair statement!).
I agree with your main point - I don't particularly want to see more discussions of social policy on LessWrong, especially when they don't push the analysis very far.
I know that there are several poly- words, including polyamory and polygamy, but am not knowledge about the distinctions. I thought polyamory was a catch-all word for "romantic relationships where people can have more than one partner, with the knowledge and approval of all other partners." Or something to that effect. And polygamy is a particular kind of polyamory where the partners are married. I could definitely be mistaken about those words' meanings, though.
Since poly was brought up by the OP in the context of gay marriage and civil unions, I used polygamy. But I certainly didn't mean to imply any sort of connotation by the use of "polygamy" rather than "polyamory."
A thought occurred to me today as I skimmed an article in a rationality forum where the subject of gay marriage cropped up; seeing as the issue has been hotly contested in various public fora and especially the courts, what about poly? After all, many if not all the arguments for gay marriage apply to poly marriage as well.
Questions for LWers who are currently in a such a relationship, or have an opinion to share:
Do polies want to marry each other or do such relationships not lend themselves to permanence above a threshold of partners? Should polies campaign for the right for a civil union anyway? what are the up and down sides of this? etc