“There is not a crisis in the city of Brownsville with regards to safety and security,” said Mr. Martinez, who has lived in Brownsville since the late 1970s. “There’s no gunfire. Most of the people that are migrating are from Central America. It’s not like they’re coming over here to try to take anybody’s job. They’re trying to just save their own lives. We’re doing fine, quite frankly.”

Unauthorized crossings along the border with Mexico have sharply declined over the past two decades, according to government data. From the 1980s to the mid-2000s, the government reported annually apprehending around 1 million to 1.6 million people who tried to cross the southwestern border illegally. That number has been halved in recent years. By month, border apprehensions averaged more than 81,588 under President George W. Bush, declined to more than 34,647 under President Barack Obama and now stand at 24,241 under Mr. Trump.

Research shows that incarceration rates of both legal and undocumented immigrants across the country are lower than those of native-born Americans, and that the net economic impact of immigration is positive.

In Nogales, Ariz., which borders and shares its name with a Mexican city, the number of violent crimes plummeted by more than 70 percent from 1997 to 2016. Similar trends can be seen in San Luis, Somerton and Yuma. The overall crime rate in Arizona has also dropped by more than a third from 1993 to 2016. During that same time, the state’s undocumented-immigrant population more than doubled, according to the Pew Research Center.