[QUOTE=Giles]
But having multiple sexual partners is generally not illegal, and polygyny is legal in many Muslim countries. Once you deal with informed consent, problems of child rearing and custody, and financial issues like health insurance, not recognising polygamy comes down to moral and religious objections.
[/QUOTE]
There is nothing right now preventing people from living in households as multiples (just as there is nothing right now, in most places, preventing gays from living together as a couple).
What is at stake is a legal status accorded to that relationship, that of marriage, which brings with it a bunch of legal rights and obligations - in respect of stuff like survivorship benefits, insurance, access to children, division of family property, support, etc. etc.
The impetus for legally recognizing gay marriage is the unfairness of treating like cases differently - that is, that a couple (of gays) looks functionally very much like a couple (heterosexual) in terms all of those legal factors noted above; the only reason not to recognize them as the same would be cultural and religious.
In contrast, a group relationship between some multiple of men and women does not, functionally, resemble a couple in this practical sense in respect of these legal factors. It would of necessity create rights and obligations different from either a gay or heterosexual couple, by the simple virtue that you are dealing with more than two people whose rights must be considered; what would be a simple binary factor becomes complex. Take survivorship. It is obvious that a marriage as such is over when one partner dies leaving the other a widow, free to remarry (and a will to the contrary presumptive heir to all property) - but what if one partner in a multiple dies?
These are not mere problems to be worked out, they are the very essence of what “marriage”, as a legal category, is - a bundle of legal rights (I’m deliberately excluding love, sex, affection, etc. because all of these exist either within or without a “marriage”). Therefore it is not obvious that fairness would dictate that polygamy ought to be recognized as a legal form of marriage simply because homosexual marriage has been so recognized. Not to say that it may not be recognized anyway, just that it doesn’t necessarily follow, and the objections to it are of a different and more practical nature than the objections to gay marriage.