While Jefferson definitely read it, almost none of its underlying philosophy crept into Jefferson's later writings as he drafted many of the documents underlying our Republic. His service record was also not on of reverance for Muslims:
https://www.city-journal.org/html/jefferson-versus-muslim-pirates-13013.html
He also wasn't impressed with how it played out in their policy at the time:
"As Jefferson later reported to Secretary of State John Jay, and to the Congress:
The ambassador answered us that [the right] was founded on the Laws of the Prophet, that it was written in their Koran, that all nations who should not have answered their authority were sinners, that it was their right and duty to make war upon them wherever they could be found, and to make slaves of all they could take as prisoners, and that every Mussulman who should be slain in battle was sure to go to Paradise."
http://www.slate.com/articles/news_and_politics/fighting_words/2007/01/jeffersons_quran.html
I don't think most people are concerned about what people are praying to - it's about how it plays out in their actions with other people. Through that lens, Jefferson was anything but tolerant with respect to the Barbary Wars. I think most in America subscribe to that point of view, articulated well here:
http://www.huffingtonpost.com/ali-a-rizvi/an-atheist-muslims-perspective-on-the-root-causes-of-islamist-jihadism-and-the-politics-of-islamophobia_b_3159286.html