The line you are quoting is from an obscure treaty of friendship with a *_*_*_*_*_*ant country that we invaded anyway (and who richly deserved it). It is not the basis of any US law.
As a little refresher for all, I have already cited the only mentions of religion in the US Constitution and the Bill of Rights. These ARE the supreme law of the land.
The Declaration of Independence has several more or less direct references to God. These are sometimes attributed to the Constitution, but that is not correct, and it is an important distinction.
"...to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them..."
"...they are endowed by their Creator with certain unalienable Rights..."
"We, therefore, the Representatives of the united States of America, in General Congress, Assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions..."
"And for the support of this Declaration, with a firm reliance on the protection of Divine Providence..."
So you see the slippery slope of dragging other documents into the discussion of the nature of American democracy. This document preceeds the Constitution and was signed by the leaders of the rebellion, including many framers of the later Constitution.
If we are going to deduce meanings from the supposed thoughts of the Founding Fathers, this would be a very significant document. However, in a legal sense, no laws can rest on the Declaration of Independence from Great Britain. They rest on our most excellent Constitution.
The Declaration was signed in 1776.
The Constitution was ratified 1787 (or as they put in writing, the "Seventeenth Day of September in the Year of our Lord one thousand seven hundred and Eighty seven"). I let that reference go as a common figure of speech.
The supposedly damning text you are citing is from the Treaty of Tripoli, 1796.
Here is the whole quote, in context:
"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."
When we see its intended purpose, it changes the meaning of the phrase, doesn't it?
But more important is that this treaty and these words are not a legal basis for anything, except friendship with the Pasha of Tripoli. We put said party out of business in 1805 anyway because he was still trying to get us to pay tribute. I guess we weren't willing to render unto so many Caesars...