"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.
Christian faith, yes, I agree.
However, it's awfully hard to separate "Christian faith" from a particular denomination once the floodgates are opened. When churches participate directly in the political process, specifically endorsing one candidate, then they have entered into a different zone. In that event, they are acting just like any other campaign source and will eventually be regulated as such.
It should come as no surprise if such politically active churches lose their tax-exempt status. If, on the other hand, a church limits their voice to opinions on specific issues, instead of a particular candidate, there can be no argument from the government. Voicing a strict opinion on issues of right and wrong is what churches do. Endorsing specific candidates is what campaign contributers do.