A more balanced take from someone who is equally skeptical of Christian and Muslim fundamentalism:
Jefferson did not demand regime change of the Barbary states, only policy change. And as far as I can find, he avoided any comment on the religious dimension of the war. But then, he avoided public comment on faith whenever possible. It was not until long after his death that we became able to read most of his scornful writings on revelation and redemption (recently cited with great clarity by Brooke Allen in her book Moral Minority: Our Skeptical Founding Fathers). And it was not until long after his death that The Life and Morals of Jesus of Nazareth was publishable. Sometimes known as "the Jefferson Bible" for short, this consists of the four gospels of the New Testament as redacted by our third president with (literally) a razor blade in his hand. With this blade, he excised every verse dealing with virgin birth, miracles, resurrection, and other puerile superstition, thus leaving him (and us) with a very much shorter book. In 1904 (those were the days), the Jefferson Bible was printed by order of Congress, and for many years was presented to all newly elected members of that body. Here's a tradition worth reviving: Why not ask all new members of Congress to swear on that?
And here's a tradition worth inaugurating: The Quran repeats and plagiarizes many passages of the New Testament, including some of the most fantastic and mythical ones. Is it not time to apply the razor and produce a reasonable Quran as well? What could be more inclusive? What could be a better application of Jeffersonian original intent?