The question is especially pertinent because so many of the people who have devised, defended and attempted to carry out Mr. Trump’s policy of identifying immigrant communities with criminality and terrorism are themselves Irish-Americans. The White House press secretary, Sean Spicer, announcing in January that his boss would continue the tradition of accepting a bowl of shamrock from the Irish prime minister on March 17, told reporters that the St. Patrick’s Day reception is “an issue that’s near and dear to me” because of his pride in his own Irish roots. Mr. Trump’s senior strategist, Stephen K. Bannon, boasts of his “blue-collar, Irish Catholic” family background. Kellyanne Conway (née Fitzpatrick) is half-Irish. Homeland Security Secretary John F. Kelly, who has the job of enforcing Mr. Trump’s anti-immigrant policies, “is remembered fondly” in Massachusetts, according to The Boston Globe, “as an adventurous Irish Catholic son who reached the highest echelons of military service.”

These are intelligent people, and it seems unlikely that they are so romantic as to imagine they’re descended from Irish kings and Celtic goddesses. Most probably, some of their ancestors were wretched people. The Irish Catholic immigrants who washed up in the United States after the potato famine of the 1840s were, on the whole, the most destitute national group ever to arrive on American shores.

They were nobody’s ideal of the desirable immigrant. The typical Irish Catholic arrival in New York or Boston was a peasant with little formal education and few material resources. Worse, these people were religious aliens — the papist hordes who threatened to swamp Protestant civilization and, in their ignorance and superstition, destroy enlightened democratic American values.

The people around Mr. Trump surely know this history, yet they act as if they were the descendants not of these poor immigrants but of the American nativists and Know Nothings who slandered and derided them. Mr. Trump’s assertion that millions of illegal immigrants voted to deprive him of his victory in the popular vote directly echoes one of the most common charges against the Irish in the 19th century: that, in the words of one Yankee, “Irishmen fresh from the bogs of Ireland” were led to the polling booths “like dumb brutes” to “vote down intelligent, honest native citizens.”

The relentless campaign to associate undocumented migrants with criminality reworks the charge that Irish Catholics were innately crooked and violent. And the demonization of Muslims as implicitly un-American reproduces the canard that Irish Catholics could not be trusted in high office because they would take orders from the Vatican. As late as 1960, John F. Kennedy faced exactly these slurs in a presidential election.