Never anything Conservative about the Kristols. Billy's father openly identified with the chief butcher of the Bolshevik Revolution.
There isn't much conservative about neoconservatives. Take away their bluff and bluster and you usually get someone ideologically aligned with Bill Clinton Democrats. In fact, Clinton was probably to the right of Kristol on some issues - for instance, unlike Kristol, the Clinton administration was willing to have illegal immigrants deported under their watch.