Should churches stay out of politics?

I've heard many strident voices declare that churches should stay out of politics. They claim that they are enforcing the First Amendment to the Constitution of the United States. They interpret this amendment to mean  that churches should be completely separate from government and therefore have no voice in anything which concerns the governing of the people. 

I am surprised by this position, for this is not what the First Amendment states. Here is the wording of the amendment:   "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof..."  .  (go here good article on the First Amendment)
The First Amendment addressed the concerns of our founding fathers in protecting against a Church/State being set up in the United States as they had seen in Europe where Church leaders also had control over the government. State churches had great power to control the lives of the people even to the point of requiring the populace to only be members of that faith. They also had the power to inflict punishments on those who did not obey their church law. The framers of the Constitution sought to protect our freedoms by adding this First Amendment to our Bill of Rights.