MANCHESTER, N.H. — Rudy Giuliani is testing many traditional political rules in his presidential run, perhaps in no way more than in his effort keep his personal faith and family life out of the race. On the stump in Iowa recently and in New Hampshire last week, the former New York mayor was asked about Catholicism and his frayed relationship with his children. Both times he said, in effect, that he’d keep his private life private. “I’ll talk about it appropriately and in a way to preserve as much as I can the privacy of my family and my children,...