You can't have a productive intra-party fight with the extremist fringe.
Because you will lose... I don't join a political party to be "bi-partisan."
I don't think it's intellectually honest or useful to demonize or dismiss those who have legitimate criticisms of Giuliani's positions.
It's the same fallacy many anti-Rudy posters use, dismissing Giuliani supporters as liberals and commies and such.