Let's allow the men who wrote the Constitution tell us it's intent:
"The government of the United States of America is not in any sense founded on the Christian Religion"
(Treaty with Tripoli, 1797. Presented by President and Founding Father John Adams, and ratified unanimously by Congress.)
"No religious Test shall ever be required as a qualification to any Office or public Trust under the United States"
(U. S. Constitution, 1787, Art. 6, Sec. 3).
"I contemplate with sovereign reverence that act of the whole American people which declared that their legislature should 'make no law respecting an establishment of religion, or prohibiting the free exercise thereof,' thus, building a wall of separation between Church and State"
(Thomas Jefferson, 1802, letter to Danbury Baptist Association).
"The civil government functions with complete success by the total separation of the Church from the State"
(James Madison [author of the first amendment], 1819, Writings, 8:432).
"Every new & successful example therefore of a perfect separation between ecclesiastical and civil matters, is of importance"
(James Madison, 1822, Writings, 9:101).
"Strongly guarded as is the separation between Religion and Government in the Constitution of the United States, the danger of encroachment by Ecclesiastical Bodies, may be illustrated by precedents already furnished in their short history"
(James Madison, undated, William and Mary Quarterly, 1946, 3:555).
"And I have no doubt that every new example will succeed, as every past one has done, in showing that religion and Govt (sic) will both exist in greater purity, the less they are mixed together."
(James Madison, letter to Edward Livingston, 1822)