Actually, as I think about it, the state does have an interest in preventing bigamy, if said bigamy is not mutually consentual. if daddy has two families and the one doesn't know about the other, the community property rights of the two clueless spouses and any children are adversely affected. If Daddy and Mommy and other Mommy all live in the same house, then the state has no interest I can see.
I agree with BT that the same principle is in play with Walker's decision to drop the legal ball and Obama's decision to drop the legal ball. It is unfortunate that Obama made the choice he did, given that I was favorably impressed with his original course of holding his nose and defending it. Obama should have let the legislature do its job and the courts do theirs, by making the justice department do theirs. Walker is in the same place. The underlying issues are different but the separation of powers issue is exactly the same - and they (Obama and Walker) are equally wrong.
As to gay marriage not affecting the institution of marriage - that is your opinion. Gay marriage advocates have long used the false premise that since an individual gay marriage does not affect an individual heterosexual marriage (or the analogous collective marriages) the institution is not affected. But that is not true. Marriage as a social institution is, by its nature, a moral issue. The values of most societies have historically dictated that if a couple is to begin to engage in rearing children, commitments must be made to protect those children and to protect the spouses (historically women) from losing their economic rights. It kept the sort of thing that is epidemic today - abandoned women, single parenthood and deadbeat dads - from being the norm.
That social dynamic has, indeed, changed. The family - which is based on the institution of marriage - has been denigrated and children and women are still bearing the brunt of that dissolution. The reason for this decline is not only the selfishness of men, but the general effacement of the principle that marriage is a sacred institution - and the basis of society. Gay marriage would further dilute the importance, sanctity and relevance of the institution - not of any particular marriage. The burden of the effacement of the family is felt in the overabundance of social programs like welfare designed to substitute for proper self-sufficient family structures. So yes, the majority is indeed effected by the erosion of the family.
The same arguments being used to defend gay marriage now were used to defend no-fault divorce and other easy-out methods in the sixties. The jury is no longer out on those issues. Lax views and laws on divorce have, as predicted, badly weakened the family and society. We've already proven that anti-family morals hurt society. This will be just as true as we weaken family structure further by redefining the entire concept.
The fact is, societies have the collective right to determine their moral value system. If the majority of people in a society wish to allow gay marriage then it ought to be allowed. But if, as has been clearly demonstrated time and again in this society, the majority wants to retain traditional marriage then it ought to be the law of the land - and the government of, by and for the people has no right to overrule the people.