The state has NOT dictated to any religions who they should consider acceptable to be married. Your issue is one of semantics only - some religious denominations technically confer "holy matrimony," but in casual speech, refer to that as "marriage," not withstanding that various political jurisdictions license "marriage" and perform "marriages" without benefit of ANY religious ritual or implications.
For example, the Roman Catholic sacrament of Matrimony doesn't extend to couples whose "marriage" is considered invalid - which can be because a partner was divorced (e.g., is married to somebody else), because a partner is not Christian and a non-clerical ceremony (or a clerical ceremony without proper dispensation) occurred, because one or both partners object to the thought of having children... all in addition to "because the partners are the same sex." So... why should we play semantic games to pretend that a same-sex union is somehow "different" or "less" than all those other cases where the Catholic Church doesn't recognize the "marriage" as "holy matrimony"? It's hard to see a reason other than pure prejudice/bigotry.
I used to argue as you do - that the civil union aspect, licensed by the county or state, should just be called that - and that only religious ceremonies should be called "marriage." But there's the problem of reality here - couples get "married" on the beach, with a ceremony conducted by a "clergyman" who may be rented, or who may have self-ordained, etc. - couples who actually practice no religion to speak of. We're going to call these "marriage" if the partners aren't the same sex, but something else if they are?
Couples who are utterly irreligious go "church shopping" to find a place for a "church wedding" - and then they never go back to that (or any) church, because they don't actually subscribe to any religion. The "church wedding" is nothing more than an opportunity to put on a show, before the REAL show, the reception.
It's just rubbish, in the United States, to pretend that even most of so-called "church weddings" represent any kind of serious religious practice. They don't.
So...let two adults who want to get married do so - let them have a marriage license and say some vows before an authorized person - Justices of the Peace, ship captains, clergy (those who may be willing to officiate such a practice for non-believers). If religious groups want to offer a sacramental or religious ceremony that accompanies the marriage... that's fine. But the religious groups don't own the word, or the practice - because the actual practice in the United States, most of the time, has little or nothing to do with religion.