The U.S Constitution is specifically secular - see Poputonian

Poputonian writes regularly on Digby's blog "Hullabaloo." He frequently discusses American history in the late 18th century with specific focus on Boston and people there such as Samuel Adams. This time he is describing the logic used by the founders when they wrote the U.S. Constitution, and what they meant when they created a secular document. Here is what he says:

The Constitution is a secularist document because of what it says and what it does not say. The first of the explicit secularist provisions is article 6, section 3, which states that federal elective and appointed officials "shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States." No religious test. This provision, much less familiar to the public today than the First Amendment, was especially meaningful and especially sweeping in view of the fact that the necessity of religious tests and religious oaths for officeholders had been taken for granted by nearly all the governments of the American states (not to mention those of the rest of the world) at the time the Constitution was written. The addition of the affirmation is significant, because it meant that the framers did not intend to compel officeholders to take a religious oath on the Bible. The intent could not have been clearer to those who wanted only religious men -- specifically, Protestant believers -- to hold office. As a North Carolina minister put it during his state's debate on ratification of the Constitution, the abolition of religious tests for officeholders amounted to "an invitation for Jews and pagans of every kind to come among us."

Notice that the statement in article 6, section 3 specifically allows Muslim Rep. Ellison to use any document he wishes to swear in as a Congressman, or no document at all (if he "affirms" rather than "swears."

But more significantly, the Constitution had to be secular because of the crazy patchwork of religions which made up the states that the 13 colonies had become. Every choice of a state religion would have caused great strife all over the nation. There was no compromise that could have satisfied most of the population.