He’s Jewish, at least by the standards of the State of Israel. Maybe his mama was a Christian or Muslim, but that would take research.
Secular Israelis don’t like digging that far, as Sharon and Bennett might be called into question.
If the state of Israel’s standards are loose enough to consider Karl Marx Jewish merely due to his descent from the rabbi of Trier (his grandfather), then those aren’t the standards to which to look.
Isn’t Bennett National Religious (Dati Leumi) himself despite the fact that he formed a coalition with secularists?