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.
"Of course it was meant to protect the government too!"
Uh, uh. No. Not in the way you mean. They specifically forbad the establishment of an official church, preventing what you fear. However, it is explicit in the writings of all the prominent men of the time that the Christian faith was expected to exert an influence in the decisions of government.