Total tangent here......
Well - a marriage ceremony is merely a ceremony - basically a means to legal status. One that every state allows to be performed by clergy, although the list of who else varies. And in the end it's just a ceremony. A state or the federal government don't really care other than that the state recognizes the marriage. They don't place a higher value on marriages officiated by clergy, or judges, civil marriage officiants, or politicians (that's actually a category in my state).
Of course many fixate on just that, while either deliberately or not so deliberately arguing about what it may mean for clergy if they're uncomfortable or refuse. It's a common reason cited for why SSM is wrong. In the meanwhile, no lawsuit has gone anywhere when a Catholic priest has declined to officiate an atheist's or protestant's wedding ceremony. It hasn't even gone anywhere in states where SSM has been legal. If anything, that's a pretty good freedom of religion exercise, whether it's about the clergy's right to decide who they will serve vs the potential married couple's "rights" to be served regardless of their religious background (or lack thereof).
I don't know if maybe we'd be better off going to the European model. Sure there can be a religious ceremony, but it's no more official to the government than having a wedding reception. The official stuff happens in front of a civil servant, and that's what makes the marriage legal in the eyes of the law.