No, no, no. One must not confuse the notion of the Biblical foundations of this nation as amply provided you in prior posts with the notion of free will and liberty of conscience. The two are not exclusive. Indeed, they are complementary.
A single thread pulled out of a rich tapestry of evidence and conduct by the Framers is no way to attempt a refutation of what is solid historical fact.
NOTE: Art VI forbade a religious test for public office and forbade nothing more.
“The clergy ... believe that any portion of power confided to me [as President] will be exerted in opposition to their schemes. And they believe rightly: for I have sworn upon the altar of God, eternal hostility against every form of tyranny over the mind of man. But this is all they have to fear from me: and enough, too, in their opinion.”
Source: Letter of Thomas Jefferson to Dr. Benjamin Rush, Sept. 23, 1800.
Source: Letter of Thomas Jefferson to Dr. Thomas Cooper, February 10, 1814.