No, the Constitution is a one-way street. It tells us what the government can and can't do. The Constitution is not a document that can be used to regulate what a Church says or does.
I believe you misunderstood my point. I am pointing out that when you allow for a greater role in government by religion, you are inevitably allowing for a greater role in religion by the government. That’s the way things have always worked, and I see no reason to think that’s going to change any time soon.