As Ralph Luker points out, the paydirt in the piece is really Allen's citation of the U.S.'s 1797 "Treaty of Peace and Friendship" with Tripoli:
As the Government of the United States...is not in any sense founded on the Christian religion--as it has in itself no character of enmity against the laws, religion, or tranquillity of Musselmen [Muslims] --and as the said States never have entered into any war or act of hostility against any Mehomitan [Mohammedan] 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.
I agree with Luker that such phrasing -- which was unanimously ratified by the U.S. Senate in 1797 -- would be inconceivable today.