For one thing, that's a woefully incomplete quote. The full quote is:"The government of the United States is not, in any sense, founded on the Christian religion."
--John Adams
"Art. 11. 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 (Muslims); and as the said States never entered into any war or act of hostility against any Mahometan (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."
Second, and perhaps most importantly, John Adams never said that.
It was actually penned by American diplomat John Barlow as Article 11 of The 1797 Treaty of Tripoli.
The Treaty of Tripoli was a treaty of peace and friendship between the US and Barbary States so that US shipping could be left alone by the Barbary Pirates (Muslims, although not all were Muslims, some where just opportunists). The Barbary States were at war with any nation for which they did not have such an agreement. As the US was in no position, militarily, to deal with the threat of every single US ship in the region being confiscated by the Pirates, the US did not want to delay any agreement by arguing the finer points of the treaty, they quickly agreed to whatever the Muslims wanted, including Article 11, and added Article 11 to the agreement. Article 11 only appears in the English version of the Treaty, and funnily enough, somehow never made it into the Arabic translation of the document, ironically at the request of John Adams himself, as he wrote about in his later years. The wording nor the sentiment of Article 11 doesn't appear in any of the treaties between the Barbary States and any other nation, either, so the Muslims singled out the US for that particular clause. Adams wasn't a big fan of Muslims. Not many people were back then, what with the Muslims having just conquered the region that became the Ottoman Empire. Adams simply refused to agree to Article 11 in the Muslim native language.
As soon as the treaty was signed, the US started ramping up, militarily, to deal with the Barbary Pirates. The First Barbary War (1801-1805) started not even 4 years after the treaty was signed, and was the first of two wars fought between the US (along with powerhouse Sweden) and the Barbary States (Morocco, Algiers, Tripoli, Tunis, or now known as Morocco, Algeria, Tunisia, and Libya). The First Barbary War ended when the Muslims became war weary after all the fighting and the blockade by the US, and, not coincidentally, after Thomas Jefferson agreed to pay the $60,000 ransom to free the captive US sailors from slavery, a move that was not well received by very many at all in the US or around the world. (I can only imagine the outrage if Obama were to do something like that today hehe).
The US then got distracted by the War if 1812 with the British (and that good-for-nothing Native American Tecumseh, who if it wasn't for him we'd own Canada), which lasted 2 and a half years. But then they went right back at it with the Muslims of the Barbary States in the Second Barbary War (then as now, not very creating in the naming of wars). The US handily defeated the Pirates with the war only lasting a few months. The war brought an end to the American practice of paying "tribute" to the pirate states and helped mark the beginning of the end of piracy in that region, and soon the European nations built bigger and more powerful ships that rendered the Barbary Pirates impotent.
But after the Second Barbary War, the original Treaty of Tripoli was renegotiated and Article 11 was dropped completely, completely nullifying the notion that its omission from the Arabic text was merely an oversight.
However, John Adams did write in 1798,one year after the first ratification of The Treaty of Tripoli, in a letter to the officers of The First Brigade of The Third Division of The Massachusetts Militia, “Our Constitution was made only for a moral and religious people. It is wholly inadequate to the government of any other.” He was talking specifically about Muslims.