Barack Obama made an impassioned pitch for Kamala Harris at a Philadelphia rally with Bruce Springsteen on Monday, telling voters: “It’s not just policies that are on the ballot, it’s who we are.

“Whether this election is making you feel excited or scared, or hopeful, or frustrated, or anything in between: do not sit back,” the former president said. “Put down your phone and vote.”

Speaking in the crucial swing state of Pennsylvania as Democrats make a final push for support, Obama – sleeves rolled up and relaxed – ripped into Donald Trump with a blend of criticism and humor. “We have to reject the kind of politics of division and hatred that we saw represented” at Sunday’s Madison Square Garden rally, where a comedian opening for Trump made a series of racist jokes.

“Here’s a good rule,” Obama said. “If somebody does not respect you, if somebody does not see you as fellow citizens with equal claims to opportunity, to the pursuit of happiness, to the American dream, you should not vote for them.”

The Democrat told the crowd at north Philadelphia’s Temple University he could understand why a Christian might be concerned about abortion rights, “but does that mean you’ll support somebody who seems to violate pretty much every precept of the Ten Commandments?” He continued: “If you’re a Muslim American and you’re upset about what’s happening in the Middle East, why would you put your faith in somebody who passed a Muslim ban?”

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Clearly enjoying himself, Obama questioned whether Trump could handle basic auto repair: “If he’s got a flat tire, he calls over his chauffeur: ‘Jeeves!’” Referencing his successor’s moneymaking schemes, he said Trump “couldn’t recite a verse but he’ll sell you that Bible” – which, he noted, was made in China. And he made hay of Trump’s claim to have “concepts of a plan” to tackle healthcare: “Honey, did you do the dishes? No, but I do have a concept of a plan to do the dishes.”

As for Harris, “she actually cares what people are going through”, Obama said.

“You may not agree with every decision she makes. You didn’t agree with every decision I made,” he acknowledged. But “if you elect Kamala Harris, she will see you. She will hear you. She will have your back, every single day.”

The ex-president spoke after Bruce Springsteen, of nearby New Jersey, played a brief set accompanied by just his guitar and harmonica. The songs – Promised Land, Land of Hope and Dreams and Dancing in the Dark – played on themes of dejection and resilience. “I’m Bruce Springsteen and I’m here today to support Kamala Harris and Tim Walz and to oppose Donald Trump and JD Vance,” the musician said. “I want a president who reveres the constitution, who does not threaten but wants to protect and guide our great democracy, who believes in the rule of law and the peaceful transfer of power, who will fight for women’s rights” and “create a middle-class economy that works for all our citizens”.

Senator Bob Casey introduced the Streets of Philadelphia singer. “His songs are like a hymnal – they’re like a prayer for our country,” said Casey, locked in his own tight race with the Republican David McCormick, as Democrats fight to hold on to the Senate. “For those watching on TV, they’re saying “Bruuuce,” he said of the crowd’s reaction to Springsteen, easy for the uninitiated to misinterpret as booing.

Another Philadelphia-linked singer-songwriter, John Legend, who attended college in the city, warmed up the crowd. Between songs, he issued a call for abortion rights and voting rights and condemned Donald Trump for “fanning the flames of hate and violence in this country”, calling the ex-president “a career con artist who’s far more interested in himself than you”.