PITTSBURGH— Abe Taleb and Jane Olszewski and their parents, all longtime Democrats in this battleground state, didn’t think twice about voting for Joe Biden in 2020. And they were all ready to do so again this year.

But the married couple and their extended families say everything changed when Israel launched its war in Gaza following the Oct. 7 attack by Hamas militants on southern Israel. Biden’s support for Israel during its military offensive has left the couple on the fence about voting for the man they helped elect four years ago. And it has left their broader family splintered: Some members argue voting for Biden is still the only way to prevent Donald Trump from returning to the White House .

“I have a very hard time imagining myself being able to pull that lever for him seeing what [Biden] has endorsed and allowed to happen” in Gaza, said Abe Taleb, 37 years old, a nonprofit recruiter. “It’d be very hard to say yes, because voting is still a tacit endorsement of that individual.”

As they gathered on a recent evening on the back patio of Taleb’s parents’ home in Pittsburgh’s Highland Park neighborhood, the couple and their parents’ discussion over dinner offered a glimpse at how many Democrats are weighing the Israel-Hamas war among other voting considerations, such as the economy and preventing a second Trump term.

Biden’s decision to continue sending weapons and other military aid to Israel, despite the high civilian death toll in Gaza and dire conditions on the ground including widespread starvation , has triggered nationwide protests and angered several key Democratic constituencies. More than a third of Democratic women and almost half of Democratic men disapprove of Biden’s handling of the war, according to a Wall Street Journal national poll in February. About half of Democratic voters under the age of 30 disapprove of his handling of the war .

For this family, though, there is one point of unanimity: Supporting Biden wouldn’t even be a question but for the war. The discontent with Biden’s handling of the war shows the political risks for the president, who narrowly carried Pennsylvania in 2020.

Taleb’s and Olszewski’s fathers have adopted opposing views: Lutfi Taleb, a 66-year-old retired educator who immigrated to the U.S. from Libya in 1978, called Biden’s handling of the war disqualifying. He plans to skip the presidential ticket and vote only in down-ballot races. By contrast, Edmund Olszewski , a 72-year-old lawyer who resides in the northern suburbs of Pittsburgh, believes there is no other option but to vote for Biden to stave off another Trump presidency.

“That’s why these guys are making me nuts,” Edmund Olszewski said of his family’s weakening support for Biden. “The very top issue is Trump. It’s simple. He frightens me.”

Abe Taleb and his wife say they are typically driven by issues such as economic inequality, but the graphic images and videos coming out of Gaza have consumed their everyday lives, particularly as parents to a 5-year-old daughter.

“Witnessing the ongoing suffering of children and fellow parents makes it even more difficult for us to simply overlook the administration’s actions here,” said Jane Olszewski, 36, who works in procurement and rejects the notion that she is aiding Trump by potentially withholding her vote from Biden. “The idea that Democrats are the only bulwark against authoritarianism and fascism is day-by-day proven less legitimate by Biden and his administration ignoring clear evidence of Israel’s war crimes and their refusal to end their unconditional support and take meaningful action to stop Israel.”

Israel has denied allegations of war crimes and has said it is taking steps to minimize civilian casualties.

The couple, who live in Squirrel Hill in the East End of Pittsburgh, try to get together with both sets of their parents at least once a month. The families are close and agree on most issues but they have debated each other on the war for months.

“Our Thanksgiving vacation, oh my God,” said Edmund Olszewski. There was at least one shouting match when the families rented a house on the Eastern Shore of Maryland for the holiday.

The grandson of Polish immigrants, the elder Olszewski’s father was a captain in the U.S. Army who served with the troops that liberated Dachau concentration camp in 1945. In March, Edmund Olszewski invoked his family history while speaking at a county government meeting in support of a local cease-fire resolution that ultimately failed.

At dinner, he said that though he wishes Biden would do more to rein in Israel, he views the president as “a pretty good guy, surrounded by good people who are doing the best they can to figure this out.”

His daughter was quick to counter. “I find it hard to believe in the face of, like, 15,000 dead kids, that there is still some greater plan at work. If there were, it has failed,” Jane Olszewski said.

The Oct. 7 attack by Hamas killed roughly 1,200 people, mostly civilians, according to Israeli officials, and saw the militant group take roughly 240 people hostage . The resulting Israeli offensive in Gaza has killed more than 36,000 Palestinians, according to Palestinian authorities. Those figures don’t specify how many were combatants but Palestinian officials and the United Nations say civilians account for most of the dead.

The Biden administration has voiced frustration with Israel’s conduct in the war but declined to back away from supporting the longtime U.S. ally. Pressure from within his party has mounted following a deadly Israeli airstrike on Rafah that Palestinian authorities said killed dozens of civilians. Biden had said a major Israeli attack on Rafah, where roughly 1.4 million Palestinians had been sheltering, would cross a “a red line” and open the door to the U.S. withholding certain types of aid. But while the White House declared the loss of lives in the Rafah strike as tragic, the administration said it didn’t merit a withdrawal of support for Israel.

“It’s like a broken record,” Lutfi Taleb said. “We’re concerned, we’re going to investigate. But it’s the same result. It’s the same action, which is none. Zero.”

Lutfi Taleb became a U.S. citizen in 1989 and save for his first presidential election in 1992, which saw him vote for independent candidate Ross Perot , has backed Democratic presidential candidates ever since.

“I used to think a lot of Biden, because he’s a statesman. He’s been around,” he said. “But the words that I heard from this man in the last six months made me go 180.”

Biden has repeatedly criticized Israel for the civilian casualties in Gaza. But the Talebs and Jane Olszewski believe the president’s comments about Palestinians have lacked the kind of raw emotion he displayed when talking about the victims of Oct. 7. “He values Israeli lives more than Palestinian lives,” said Abe Taleb.

“I don’t believe that,” Edmund Olszewski interjected. He added that Trump’s comments on the war —which have included threats to deport pro-Palestinian protesters and ban Palestinian refugees from the U.S., as well as general support for Israel’s offensive—suggest the former president would be far worse than Biden on the issue.

Lutfi Taleb came back with: “[Biden] can’t come and tell me, ‘I’m not that great, but the other person that’s running for president is worse.’”

He added: “Well, if it’s gonna take four bad years of somebody else for [Democrats] to wake up and change course, then so be it.”

Many households in Squirrel Hill display “We Stand with Israel” yard signs. The neighborhood was the site of the deadliest antisemitic attack in U.S. history in 2018, when a gunman killed 11 worshipers at the Tree of Life synagogue.

Jane Olszewski and Abe Taleb have sought to distribute pro-Palestinian yard signs that read “Stop Genocide. Free Palestine.” But when she posted about the signs in a Facebook mom’s group, the administrators removed the post after some of the group’s members suggested it was antisemitic, which the couple denied. The climate surrounding the war has created distance within some of their friend groups.

On Friday, Biden outlined a previously nonpublic Israeli proposal for a cease-fire and exchange of Israeli hostages and Palestinian prisoners and called for an end to the fighting, marking his biggest push yet to bring the war to a close. Both Abe Taleb and Jane Olszewski agree a fundamental shift in Biden’s policy toward Israel could persuade them to back him once more in November. But they are doubtful such a change will come to pass before the election.

Everyone seated around the table knows they will come back to the subject many more times in the next five months. Some of them may simply agree to disagree come Nov. 5.

“I’m just glad it’s gonna happen before Thanksgiving,” said Lutfi Taleb.

Write to Sabrina Siddiqui at sabrina.siddiqui@wsj.com