WHEN is a Jew not a Jew? When he’s a Karaite. Or so says Israel’s chief rabbinate, which, after 65 years of relative harmony with an ancient Jewish sect, is reopening an old and bitter schism. In recent months, rabbis working for Israel’s ministry of religion have deemed Karaite marriages invalid, fined their butchers for claiming to be kosher, and demanded that Karaites marrying Orthodox Jewish women should convert, sometimes having to undergo tavila, or baptism. “We are already Jews,” protests Moshe Firrouz, a computer engineer who heads the Karaites’ Council of Sages. “The rabbinate is denying us our religious...