Is it not the law-of-the land?
The Treaty of Tripoli? The one that has the famous phrase "the Government of the United States of America is not in any sense founded on the Christian religion" is certainly not law of the land. First, this phrase is actually not even in the original Arabic, but only the English translation, and I don't think anything that isn't in the version of the treaty both sides agreed to is in any way binding. Second,
given the full context is:
"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."
The point, therefore, is simply to say that the United States (the government) doesn't have enmity towards the Muslims for not being Christian. This would seem to not do anything more in terms of US laws than the First Amendment.
Finally, and perhaps most importantly, the original treaty that this phrase was found in was abrogated less than a decade later
and replaced with a new one that did not include the applicable phrase. So
even if that phrase was law of the land, it was only the case from 1797 to 1805.
Now, some use the phrase in this treaty not to try to argue it means anything legally, but that the fact it was passed showed attitudes towards religion in the government (even if not in the original Arabic, the phrase was found in the English presented to Congress). Now, as I noted, I don't think it would mean anything more than the First Amendment already says, but I do not think passing the treaty that had the phrase means much in terms of what the people in government thought about the subject. They were desperate to stop the attacks on US ships by the pirates (the whole purpose of the treaty was to get Tripoli to reign in the pirates, as US ships no longer could rely on British ships for protection) to the point they were agreeing with a treaty to pay them a lot of money to make the attacks stop. What was Congress supposed to do, even if they had disagreement on it--send the treaty team all the way back to renegotiate the treaty to remove that one phrase that wasn't particularly important to the treaty, then have them come all the way back, which would have taken months given the slow travel pace back then, all the while the pirates were attacking US ships and kidnapping Americans?
The Treaty of Tripoli is sometimes used as a bit of a "gotcha!" but I don't think it means anything more than the Supreme Court decision
Church of the Holy Trinity v. United States referring to the US as a "Christian nation".