The much-bandied about phrase “separation of church and state” means different things to different people. To those from the secular humanist persuasion, it means that the state can make no public acknowledgement of religion, have no religious displays, recognize no tax exemptions for churches, and goes so far to regulate even religious expressions of private individuals in the public arena out of line. One also hears that any attempt by others to “moralize” or use any religious values to argue for a policy should be silenced.
On the other hand, there are those who believe the matter is simply that the government should not establish an official state church, or that a church should not be anointing officials in the government. Other than that, people should believe and practice how they see fit. Both sides couch their arguments on constitutional theories, some involving Thomas Jefferson’s "wall of separation" letter.
To consider this issue, it is important to look at the historical situation of the framers and what they intended. To recap, they were declaring independence from the King of England. There is one important title for the monarch of England that is relevant to this issue, “Supreme Governor of the Church of England”. Not only was the Church of England the official state religion (and still is), but the King himself was the head of that Church. This ensured that his political reach not only extended in the public realm, but from the pulpit. The hierarchy of the church was subservient to the king. This led to abuses in both directions, those by the church and those by the government.
The founders did not declare independence from England because they wanted to set up a secular state. They declared independence because of a long train of abuses and usurpations of government power against its people. They were concerned about matters of tyranny, not theology. The Boston Tea Party was about taxes (and thus enshrined in American tradition the fine art of bitching about taxes), not about Baptists throwing Presbyterian’s Bibles into the Atlantic. The Declaration itself made liberal use of religion in general, as did the Founders in their public statements. Even in Jefferson’s Wall letter, he expresses religious sentiment and asks for prayers. It’s obviously clear; it isn’t religious expression they are worried about.