I've certainly heard the argument that polygamy is tied into oppressive social structures, and therefore legitimizing it would be bad.
Same argument can and has been applied to other kinds of marriage.
On the one hand, the argument doesn't need to be correct to be the (or a) real reason. On the other, I'd expect more people to be more convinced that polygamy is more oppressive (as currently instantiated) than vanilla marriage (and other forms, such as arranged marriages or marriage of children to adults, are probably more strongly opposed).
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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