Okay, let's get one thing straight:
From a legal standpoint, marriage is not a right. It's a privilege. Just like driving and concealed carry in most states. Anything you're required to have a license for is not a right, it is a privilege.
States require licenses for you to get married and thus, it is not a right. It is something the state, by virtue of its magnanimity, may permit. But rights are things that you can do without any bureaucrats' permission. Rights are something that require no consent from any other person than yourself.
When gay marriage is concerned, those who promote it are not demanding equal rights, they are begging for equal privilege. They want the state to endorse or condone them -- which is something that the state may or may not do according to its whims. They want to be coddled by the state like it were some loving, supportive parent who says "Whatever you decide, we're 100% behind you!"
If you think marriage is your right, then you should want the government out of it. From a legal stand point, this means you push the matter entirely into the purview of contract law. You remove licensing, tax quirks, and all those other weird legal idiosyncrasies that have been attached to the matter and leave it be.
If one church prescribes a certain kind of contract as acceptable marriage, that's their decision. It won't be a matter of church meddling with state. It will be a church offering its consent. This, in no way, violates the principles advocated in the First Amendment.