"This is entirely unconstitutional! Remember that the separation of church and state goes both ways!"
Actually, it doesn't. It was intended to protect church against state only; never the other way round.
To say that the Constitution prevents churches from interfering in government is just dead wrong.
Of course it was meant to protect the government too! For the most powerful church to control the government means a very short step from that church becoming the ONLY church. History is chock full of good examples of why it's a bad idea. The leadership of the Church of England being in such control of things pre-U.S. independence probably had something to do with that particular part of the Constitution. It has to be a two-way protection, or it is no protection at all.