I currently know of no state that doesn't already have "exclusive" rights to issue marriage licenses, so, in effect, the state already has control over marriages (actually for this purpose should be "weddings"). Yet, the state already has prescribed rules of marriage ministers, priests, and rabbis must follow if they're to avoid penalty from the states.
This coupled with the infringement of federal judges into state issues like recently occurred in Alabama, and we have the making of the Supreme Court redefining marriage without any consult of the American people.
So, do states cross a line of "respecting an establishment of religion" in presetting requirements for marriage? "Congress shall make no law" should clearly prohibit the Federal courts' intervention, but is no guarantee of their exclusion. Since only states issue marriage licenses, should ministers, priests, and rabbis only have authority to "bless" the marriage act - done by the "state", with a wedding ceremony from the "church" and each specificly pass laws to exclude federal judiciary involvement? Or should states stay out of marriage altogether, except for the purpose of recording and keeping vital records and leave the issue of marriage definition to religious institutions?
Let me put it this way: Anton LaVey was licensed to perform weddings.
Most states only require that one be a "licensed minister," and there are at least a couple of organizations that will "ordain" just about anybody. And if you, like LaVey, found your own religion, you get ordained by them and Presto!
State establishment would come from something like saying, "Sorry, only protestant marriages are recognized in this state" or "Moonies can't perform weddings."