Neo-Cons are not conservatives at all, but a mixed group of idealists, former Trotskyists, social engineers and beneficent imperialists, with no particular attachment to tradition, who wished to remake the world in America's image. Their project had a kind of blind virtue to it, and loads of faith.
Neo-cons believed in 2003 (and still do), that the Arab world, given a chance, would embrace liberal democracy. It would work in Iraq, and then, by force of example, it would catch on, like a happy contagion, throughout the region.
They are establishment Republicans!!!!