In 1903, Judge magazine, a satirical weekly with a Republican bent, published a political cartoon with the caption, “The Unrestricted Dumping-Ground.”

The image shows Uncle Sam staring out at the ocean as swarms of immigrants, depicted as armed rodents, exit passenger ships from southern and eastern Europe and swim ashore. The vermin have human heads with swarthy complexions, and they wear hats or bandannas labeled “Mafia,” “Anarchist” and “Socialist.” One carries a sword that reads “Assassination” on the blade. Another holds in his teeth a gun with “murder” inscribed on the grip.

Looming off in a corner of the drawing is a likeness of President William McKinley, who had been assassinated two years earlier by Leon Czolgosz, an anarchist. Czolgosz was not an immigrant; he was born in Detroit to parents who had migrated from Poland. But that detail didn’t stop McKinley’s successor, Teddy Roosevelt, from using the assassination to call for what today might be described as extreme vetting. “They and those like them should be kept out of this country,” said Roosevelt in his eulogy of McKinley delivered to Congress. “And if found here they should be promptly deported to the country whence they came; and far-reaching provision should be made for the punishment of those who stay.”

The late 19th century had seen the start of the second great wave of immigrants from Europe, and Roosevelt understood that resistance to these newcomers was growing. More than 25 million people arrived in the U.S. between 1865 and 1915. But they were no longer coming mainly from places like England, Ireland, Germany and Scandinavia. The more recent immigrants were Italians, Poles and Russian Jews, who some saw as upsetting the country’s social balance. Their different religions and political traditions provoked fears and anxieties among the native-born population that politicians were happy to exploit. Roosevelt’s Republican Party didn’t mind his—or Judge magazine’s—conflation of immigration and homeland security because it was concerned that too many of these latest arrivals ultimately would vote Democratic.

After the terrorist attack in New York City last week, President Trump called for shutting down the annual diversity visa lottery that Sayfullo Saipov, an Uzbek native, used to enter the country. Our current immigration system favors people with family or job connections in the U.S. The lottery was implemented, with bipartisan support, in the early 1990s for people who have neither. Congress had abolished country quotas back in 1965, effectively ending the European dominance of U.S. immigration. Over the next 25 years, mostly Latin Americans and Asians came instead. The intent of the new lottery was to diversify the stock of newcomers. ...