The 1796 Treaty of Tripoli was signed to protect the US merchant fleet from Barbary Coast pirates before we had sufficient naval forces to do the same and stop paying tribute to them to let our merchant ships pass. We therefore wanted to distinguish the US from Christian European nations which were considered by Muslim nations in religious conflict with them. The bottom line is that when you read the entire article in context it shows that the intention of the line was not to say that the nation was not founded upon Christian principles but to assure safe passage.
Let us read a few quotes from John Adams to illustrate the point that our founding fathers were intent on founding a Christian nation with room for all religions and even atheist and secularists.
"Statesmen my dear Sir, may plan and speculate for Liberty, but it is Religion and Morality alone, which can establish the Principles upon which Freedom can securely stand . . . The only foundation of a free Constitution, is pure Virtue, and if this cannot be inspired into our People, in a great Measure, than they have it now, they may change their Rulers, and the forms of Government, but they will not obtain a lasting Liberty."
"The general principles on which the fathers achieved independence were. . . the general principles of Christianity. . . I will avow that I then believed, and now believe, that those general principles of Christianity are as eternal and immutable as the existence and attributes of God; and that those principles of liberty are as unalterable as human nature."
Under Pres. Thomas Jefferson in the early 1800s we had sufficient naval and marine forces and the will to defeat the Barbary Coast pirates from Morocco to Tunisia to the shores of Tripoli. We ensured the free passage of merchant ships along the North African coast and put an end to paying tribute.