"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 Mussulmen; and, as the said States never entered into any war, or act of hostility against any Mahometan 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."
Article 11, the Treaty of Tripoli (the Treaty of Peace and Friendship) signed 1796.
The above passage is of particular significance because as part of a treaty it was ratified by the U.S. Senate (unanimously) and signed by the President so it had a certain amount of legal force (until the treaty was broken). The passage is also especially relevant in the present case because it explicitly refers to Islam (although in somewhat dated terms). On the other hand, the famous phrase "wall of separation between church and state" was never legally binding in the same way and instead comes from a letter written by Thomas Jefferson giving his interpretation of the establishment clause (i.e. "Congress shall make no law respecting an establishment of religion...").
In any case, the treaty is clear. "... the Government of the United States of America is not, in any sense, founded on the Christian religion". And Prager's tirade is cut off at the knees.
But as silly as Prager is, he does make me think about certain deeper issues. For example, when it comes to politics in the Muslim world (e.g. Algeria, Turkey, Iraq after the dust settles), I feel like I definitely need to think through some of the details, but I generally feel like the best kind of government would somehow combine democratic reforms and large helpings of Islamic law. It only makes sense. If you are in a part of the world where most of the population consists of religious Muslims and you set up a government there which is responsive to the values, beliefs, hopes, aspirations and interests of the people, then you should expect the government to be "Islamic" to some degree.
So when I look back to Prager's piece, I'm not really objecting to the idea of a religious state per se but I'm mainly making the legal/historical objection that U.S. was neither set up nor intended as a "Christian nation". Religious states certainly have their own special sets of dangers and temptations but at this point I wouldn't categorically throw out the baby with the bathwater.