That's the way it is now. There's nothing in the legal system about a religious significance to marriage. It's really a civil status, with lots of effects on tax, inheritance, medical responsibility. Most marriages happen in churches, but it's the church that adds the religious significance. But you can also have non-religious marriage. The idea of separate but equal civil unions for gays was solely intended as an insult to gay unions. Assuming they were really equal, there was no legal difference.
Actually, there is a difference regarding what @9Rock9 is saying.
The state can get completely out of the game of designating anything a "marriage," including enforcing any presumed "contractual" agreements the concept might entail. The state simply becomes completely agnostic to the term, such as it already is now with "godparent."
But the state does recognize and enforce "domestic partnership" contracts made between any two or more consenting adults, within the state's contract law statutes. The domestic partnership contract would stipulate all necessary legal performances expected of each party, and it would be the basis for any further joint commercial concerns, such as insurance, bank accounts, mortgages, hospital care, et cetera.
If any two or more people want to be socially known as "husband" or "wife" or whatever to anyone else, they would have find an agreeable clergycritter to hold the ceremony. Nobody outside their own social circle need be impacted or even care. There would not be a state marriage certificate for them to sign, but if they want to get something printed on their own to hang on the wall, that's their decision.
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