The other peculiar thing about BiBi is that aside from his (in)famous reputation, he is considered a moderate in Likud and the Israeli right-wing in general.
Yup. He likes to sit in the middle, ideologically speaking, of his coalitions. Of course, moderate here is a very ill-defined term. In Israel, being "moderate" means your views aren't as emotion fueled. I don't think there is much that separates Bibi and people like Danny Danon on foreign policy besides rhetoric.
In terms of religiosity, he is definitely one of the more moderate Likudniks (He's essentially Israel's Newt Gingrich, marriage wise.