He went on to criticize Ms. Winfrey’s interview with Ms. Harris on Thursday — which featured a number of celebrities and drew hundreds of thousands of viewers — writing, “I couldn’t help but think this isn’t the real Oprah.”

Mr. Trump has claimed before that he appeared in the final week of “The Oprah Winfrey Show,” an assertion that has previously been debunked. CNN reported in 2020 that Mr. Trump had made the claim at least four times as president, and that he had been making it since at least 2013. Mr. Trump did appear on the show during its final season but not during its last week, which became a big television event.

Mr. Trump last appeared on Ms. Winfrey’s show on Feb. 7, 2011, three and a half months before the show ended, with his wife and children, according to archived television listings. The final week of her show, in late May of that year, featured Tom Hanks, Tom Cruise, Madonna, Jamie Foxx, Stevie Wonder, Michael Jordan, Aretha Franklin, Will Smith and Jada Pinkett Smith, according to the listings.

Mr. Trump’s campaign did not respond to a request for comment on Sunday. A spokeswoman for Ms. Winfrey declined to comment.

Ms. Winfrey endorsed Ms. Harris this year and spoke at the Democratic National Convention last month. Her livestreamed interview with Ms. Harris on Thursday night featured celebrities including Chris Rock, Jennifer Lopez and Meryl Streep.

The latest jab came from Gov. Sarah Huckabee Sanders of Arkansas. This past week, she took the stage at a campaign event for former President Donald J. Trump and declared that her three children had given her the sort of humility that is important to maintain in national politics.

“My kids keep me humble,” she said to the crowd. “Unfortunately, Kamala Harris doesn’t have anything keeping her humble.”

Call it the motherhood divide. The presidential race has exposed a fault line in American culture — or at least among today’s most prominent politicians — over the deeply personal (and usually private) decision to have children. With an election likely to be decided by razor-thin margins, perhaps by women whose votes could tip the scale either way, motherhood itself has become a campaign-trail cudgel.

Conservatives are trying to appeal to voters who may see an existential value in motherhood. Prominent Republicans, including Senator JD Vance of Ohio, Mr. Trump’s running mate, have tied their concerns about reproduction to the declining birthrate in the United States, disparaging childless women like Ms. Harris in the process.

“This is not about criticizing people who, for various reasons, didn’t have kids,” Mr. Vance said in an interview with the commentator Megyn Kelly in July, addressing past comments he had made calling Ms. Harris and other top Democrats “childless cat ladies” without a direct stake in the country’s future. “This is about criticizing the Democratic Party for becoming anti-family and anti-child.”

Democrats report having fewer children than Republicans do. According to a 2022 survey by the University of Chicago, about 38 percent of Democrats had never had children as of that year, compared with 26 percent of Republicans. But those numbers do not back up claims that the Democratic Party is dominated by people without children or families.

A majority of American families are also considered nontraditional. More children are raised by remarried parents, single parents, cohabitating parents or no parents than by two parents in their first marriage.

Some Republican strategists do not see a winning strategy in broadsides against people who might not have children.

“When you attack anyone for their identity, you offend everyone who shares that identity,” said Whit Ayres, a longtime Republican pollster. “So if you attack people for being childless, you offend everyone who has never had children. For whatever reason.”

In the opposite corner, the left is trying to appeal to women who see motherhood as valuable — but still a choice.

Democrats have framed the decision not to have children as part of a set of choices that people should be able to make in private. And they have argued that many Americans are declining to have children because the government is not providing adequate services, like affordable child care and quality maternal health care.

In an appearance on Thursday with Oprah Winfrey, Ms. Harris pointed to the story of Amber Thurman, a 28-year-old mother from Georgia who died after not receiving prompt treatment when she experienced complications from a medication abortion.

“It’s a health care crisis that affects the patient and the profession,” Ms. Harris said, blaming abortion restrictions enacted after the fall of Roe v. Wade in 2022 — a development that Mr. Trump has celebrated.

Ms. Harris has not directly responded to Republicans who have accused her of not caring about families because she does not have biological children of her own. Members of her blended family are doing the work for her.

“It’s appalling for somebody who is in a position of leadership, like governor, to say something so repulsive and so out of touch,” Doug Emhoff, Ms. Harris’s husband and the father of the vice president’s two stepchildren, Cole and Ella, said in an ABC News interview this past week of Ms. Sanders’s comments. “As if you need to have your own biological children to be humble. But then — then to say as if women should be humble,” he added.

Mr. Emhoff’s ex-wife, Kerstin Emhoff, also responded to Ms. Sanders on social media: “Kamala Harris has spent her entire career working for the people, ALL families,” she wrote. “That keeps you pretty humble.”

Anya Jabour, a professor of history at the University of Montana who studies gender and politics, said reproductive status had long been used to minimize women in politics.

She said that “cat lady” was an old trope: Opponents of the American suffrage movement used cats to symbolize femininity, and depicted men as stuck at home with the animals should women win the right to vote.

Dr. Jabour said that there was a “long history of a false dichotomy between feminism and maternalism,” or people whose ideas of identity revolve around motherhood.

She added that cases like Ms. Thurman’s in Georgia showed that “in fact, reproductive rights and mothers’ interests are very closely intertwined.”

But many of their smiles shrank when they were asked about the embattled Republican nominee for governor, Lt. Gov. Mark Robinson, who has been under fire since CNN reported this week on the lewd comments he made on a pornography website several years ago. According to CNN, Mr. Robinson wrote on the site that he was a “black NAZI,” that he enjoyed watching transgender pornography and that slavery was not bad. He also recounted on the site how he went “peeping” on women in public gym showers as a teenager.

Few rally attendees believed the article about Mr. Robinson, who had already faced criticism for old Facebook posts that were widely condemned as racist, antisemitic and transphobic. And while many voters said they would still stand behind him, some acknowledged that the allegations were damning.

“Look, he’s toast,” said David Huffman, 60, of Wilmington, who wore a collared shirt printed with the American flag. “I’m still going to vote for Mark, but at this point it’s worse than a Hail Mary.”

Not only was Mr. Robinson not at the rally, but Mr. Trump also did not mention his name once to the thousands of supporters who were in attendance, the very people who helped fuel the rise of the lieutenant governor in 2020.

Those who stood firm on voting for Mr. Robinson used the same defense that he deployed this week: It was all fake, and the news media could not be trusted.

Other supporters offered Mr. Robinson some grace.

“If it’s true, we all got a past, and some of us got a past we aren’t proud of,” said Jason White, 41, of Columbus County. “People can change.”

Quintina Debose, 41, of Wilmington, said: “People do stuff all the time. They just don’t get caught.” The latest allegations, she said, were just a meaningless distraction.

But for some conservatives, the revelations were deeply concerning. Even if Mr. Trump won the state in the presidential election, they said, the chances for success for Mr. Robinson seemed less likely.

Thomas Hart, 31, of Wilmington, said he was sure about voting for Mr. Trump because his previous first choice, Robert F. Kennedy Jr., had endorsed the former president. That feeling does not extend to Mr. Robinson, though, because he has made some “pretty wild” remarks, Mr. Hart said.

Still, this was a Trump rally, and many remembered the support that the former president had shown Mr. Robinson in the past.

Bryan Faulcon, 39, of Wilmington, said he didn’t believe the allegations, but even if they were true, Mr. Robinson still had his vote. The calculation was simple, Mr. Faulcon said: policy over character.

“They can’t take him down,” he said.

The answer? He wouldn’t.

Speaking for just over an hour at a boisterous rally on an airport tarmac in Wilmington, N.C., Mr. Trump made no mention of Mr. Robinson or the scandal surrounding him, even as he gave shout-outs to a number of the state’s officials and politicians. And Mr. Robinson, who has denied the accusations, was conspicuous by his absence.

Instead, Mr. Trump delivered a fairly standard rally speech, attacking Vice President Kamala Harris and the Democrats on the economy and immigration while digressing to criticize Ms. Harris’s livestreamed event this week with Oprah Winfrey; to call her running mate, Gov. Tim Walz of Minnesota, “weird”; to say that he would ask Elon Musk to help him send rockets to Mars; and to claim falsely that an Olympic boxer was transgender.

One of the only speakers at Saturday’s rally to acknowledge the controversy engulfing Mr. Robinson was Representative Dan Bishop, the Republican candidate for state attorney general, who called the revelations “a meticulously timed and coordinated character assassination.”

Building on his effort to make immigration, an area where voters are dissatisfied with Democrats, the central issue of the presidential campaign, Mr. Trump announced that he would push Congress to pass legislation outlawing so-called sanctuary cities, places that limit how local law enforcement can cooperate with federal immigration authorities. During his presidency, Mr. Trump issued an executive order that tried to withhold federal grants to such locales, an effort that was blocked by federal courts.

Mr. Trump, who has vowed to conduct an enormous deportation operation if elected, said he would deploy federal law enforcement agencies to “hunt down” and “capture” those in the country illegally.

But Mr. Trump omitted any mention of Haitian migrants in Springfield, Ohio, a group that he falsely claimed at the presidential debate this month had been eating people’s pets. On Wednesday night, Mr. Trump said he planned to visit Springfield in the “next two weeks.” Gov. Mike DeWine of Ohio, a Republican, wrote in a guest essay in The New York Times on Friday that as a supporter of Mr. Trump and his running mate, Senator JD Vance of Ohio, he was “saddened by how they and others continue to repeat claims that lack evidence and disparage the legal migrants living in Springfield.”

Faced with polls that have showed him losing ground to Ms. Harris with female voters, Mr. Trump made a direct appeal to women, repeating claims that he had made in a lengthy all-caps social media post overnight, insisting that women were “more stressed and depressed and unhappy than they were four years ago.”

Mr. Trump has taken credit for appointing three Supreme Court justices who voted in 2022 to overturn Roe v. Wade, which eliminated the constitutional right to abortion and led to bans or abortion restrictions in 22 states. A large share of voters in swing states, particularly women, have said abortion will be central to their decision in November. But as he spoke about women at the rally, Mr. Trump said, “You will no longer be thinking about abortion, because it is now where it always had to be, with the states and with the vote of the people.”

Mr. Trump also repeated the false claim that his political opponents support the “execution of a baby after birth.” Infanticide is illegal in all 50 states.

Dante Murphy, a Baptist minister who lives in Wilmington and was standing conspicuously behind a news media section at the rally, sported a “Mark Robinson for Governor” T-shirt and a baseball cap signed by him. While he continued to support Mr. Robinson, he said, Mr. Trump’s avoidance of the topic made perfect sense.

“You know, he is playing it safe by just being quiet right now,” he said.