First Amendment. The State can’t touch the church in this issue.
The State, however, can say that the church can’t issue marriage (or civil union) licenses because that is a church/state issue.
You're joking, right?
The state can make up all sorts of excuses. As long as they know that they will get away with doing something and still remain popular and elected, they will do it.
If you believe this you are in for a big surprise. The Bill of Rights means NOTHING. It should now be called the Bill of Suggestions or the Bill of You Can do that-—for now peasant.