Please consider the Treaty of Tripoli, which was signed by congress and the president unanimously, and many of them were at the original Continental Congress and Constitutional Conventions. It was ratified June 7, 1797. The revolution and why we had it was still fresh in everyone's minds and most of the founding fathers were still active in politics.
ARTICLE 11.
As the government of the United States of America is not in any sense founded on the Christian Religion,-as it has in itself no character of enmity against the laws, religion or tranquility of Musselmen,-and as the said States never have entered into any war or act of hostility against any Mehomitan nation, it is declared by the parties that no pretext arising from religious opinions shall ever produce an interruption of the harmony existing between the two countries.
The muslims of Tripoli were nervous that the Americans would use their religion as an excuse to discriminate and even presecute another crusade. This tells us, as well as other things, that the founding fathers almost unanimously agreed that religion has no place in government.
The myth that that phrase is in the Constitution is legitimate, but the intention is not.
http://www.yale.edu/lawweb/avalon/di...y/bar1796t.htm