WASHINGTON — When Joe Biden came of age, he saw Israel as a besieged state that was a haven for a persecuted Jewish minority, a worldview that stayed with him through his 36 years in the Senate and his rise to the presidency. Biden often recalls in public speeches what former Israeli Prime Minister Golda Meir told him 50 years ago: “We have nowhere else to go.” Today, a faction of Biden’s party sees Israel very differently: as a military colossus run by far-right officials who’ve suppressed Palestinians and denied them basic freedoms. These dueling perceptions are the root of...