Donald Trump has decided to double down on his insults of Mexicans living in the United States. Talking to CNN’s Anderson Cooper this week, he said he had nothing to apologize for.

In case you were vacationing on a desert island for the past month, this is what he said: “When Mexico sends its people, they’re not sending their best . . . They’re sending people that have a lot of problems, and they’re bringing those problems with us [sic]. They’re bringing crime. They’re rapists. And some, I assume, are good people.”

The remarks have cost Trump financially, as one after another high-profile individual and corporation abandons ties, but not politically with some GOP primary voters.

He’s now either second or first in national polls and in the important primary states of Iowa and New Hampshire, though it’s important not to overstate the size of his base. We’re still talking barely into double digits, 12 percent to 16 percent nationally.

In his original remarks, Trump made no distinction between legal and illegal immigrants, though he and the media have treated the insults as if they referred only to illegal immigrants from Mexico.

The point is an important one — in fact, Trump and many who think as he does conflate the population. They are not just anti-illegal immigration; they are opposed to immigration overall, especially from Latin America.

This is certainly true of groups like the Center for Immigration Studies, the Federation for American Immigration Reform and NumbersUSA, whose goals are to reduce legal immigration of both low-skilled and high-skilled immigrants.

Their ultimate objective is to reduce population overall, as they make clear in their many position papers on the negative impact of population on the environment.

Oddly, conservatives have made common cause with these groups, whose roots are in the population-control and environmental movements, hardly in tune with conservative values.

But what about Trump’s contention that Mexico is sending us criminals and rapists? In fact, the very opposite is true. Mexican immigrants, legal and illegal, like all immigrants, have lower rates of criminal behavior than the native born.

At the very time that immigration, including illegal immigration, was going up, crime was going down.

As a new study from Walter Ewing, Daniel Martinez and Ruben Rumbaut points out, the foreign-born population rose from 7.9 percent to 13.1 percent from 1990 to 2013, and the number of unauthorized immigrants more than tripled, but the violent crime rate declined by 48 percent and property crime by 41 percent.

This phenomenon has been studied thoroughly in so-called gateway cities, such as Miami, El Paso, San Antonio and San Diego, which attract large numbers of newcomers.

Of the top 10 safest big cities ranked by Congressional Quarterly using FBI statistics, fully seven have very large Hispanic immigrant populations.

El Paso, with its 81 percent Hispanic population, including 26 percent who are foreign-born, has ranked as the safest large city in the US for several years. This fact is all the more amazing given that Juarez, a mere dozen miles across the border, is one of the most violent places in the hemisphere.

As for incarceration rates, immigrant men ages 18 to 39 are less than half as likely to be incarcerated than native-born men the same age, according to the Ewing study.

Mexican men are even less likely to be incarcerated: Their rates are one-third that of natives with similar demographic characteristics.

And Salvadoran and Guatemalan men are incarcerated at one-fifth the rate of native-born men without a high school degree — the group most likely to commit violent crimes.

There’s a reason for this, and it has been true throughout the history of our country.

Immigrants are self-selected, even those who come here illegally. They are not the richest — not “the best,” as Trump suggested — but they are the most motivated.

They come here to work, which is why Mexican-born males participate in the labor force at substantially higher rates than whites, 88 percent to 71 percent.

Trump won’t win the GOP nomination, any more than immigrant-bashing candidate Herman Cain did in 2012. Cain jumped to first in the polls, too, when he started talking about warning illegal immigrants they would be shot on sight in a Cain administration.

But Republicans should be worried, nonetheless. Trump’s bigotry will further damage the party and could end up costing it the White House.