Yes, there are many governmental actions contracted out to private organizations. No, they don't all need to become public (although some should).
Take private schools. If you want to be able to discriminate about who or what you teach and you are a private school, that's perfectly fine. You get no subsidies, no vouchers, no special tax breaks. And, if you don't teach approved subject matter, no official accreditation. I'm sure plenty of private schools would function effectively under those terms, and could be excellent schools.
So what's the difference, you ask. In the case of the private school, the business is providing a product and there's no harm (except maybe to some students) in letting the market decide the value of that product.
But in the case of marriage, what's being provided is approval of a contract that is binding on more than just the people getting married. It's a societal commitment that provides benefits that have to be honored or paid for by other members of society. Why should bigots who refuse to apply the laws equally to all be entrusted with that power?
Those religious organizations who don't want to apply the law equally shouldn't be in the position to apply that law at all. Let them perform their private bonding rituals as they see fit and let the market decide how much to value their "marriages" - if at all.
Some of us might not place much value in marriages performed by snake worshipers who speak in tongues, for example.
