Trump’s grip on the base is probably secure, but at least one of his minions is making his constituents shift uncomfortably in their seats.

ORANGE CITY, Iowa — A year ago, Evan Wielenga, 40, believed — as does his congressman, Steve King — that undocumented immigrants should all be deported. They broke the law to enter the country. They spoke little English. They strained schools and public services.

But as talk of a border wall and a Muslim ban overtook the presidential campaign, Mr. Wielenga, the agronomy manager of a farmers’ co-op here in northwestern Iowa, had a change of heart.

He heard dairy farmers say they couldn’t get their cows milked without immigrants. “You can put an ad in the paper and you won’t get two white guys to apply,” said Mr. Wielenga, who grew up on a dairy farm himself.

He heard of the ruinous damage an immigration raid had done to families. “Some of these kids were born in the U.S.,” he said. “These families had lived here 10 years, and all of a sudden, Dad’s gone, Mom’s gone. When you think of it from that perspective, what’s the lesser of two evils?”

Mr. King, a Republican who has displayed a Confederate battle flag on his desk in Washington, shows no sign of budging in his views. His latest anti-immigrant tirade — “We can’t restore our civilization with somebody else’s babies,” he said — once again drew wide condemnation and critical attention to Iowa’s Fourth Congressional District, whose voters overwhelmingly re–elected him to an eighth term in November.

Sioux County, Mr. Wielenga’s home, provided the largest margin in the 39-county district, Iowa’s most conservative. And there is no shortage of voters who echo Mr. King’s contention that “culture and demographics are our destiny,” as he said earlier this month to cheers from white supremacists.

But in conversations over four days with residents who voted for Mr. King, a new chorus of earnest naysayers could also be heard in many corners of the district. Some said the congressman’s latest provocation — uttered in support of a far-right Dutch politician — was finally more than they could brook. Several said they were rethinking their support.

“I’ve always voted for him, but I think this was way out of line,” said Bill Kooi, a retired farmer, sipping coffee at a Hardees in Orange City, as the friends who shared his table — to a man, older white conservatives — all nodded.

Again and again, voters brought up how much Mr. King’s district has changed since his election 15 years ago. Though still overwhelmingly white, it has absorbed a sizable population of Hispanics who have taken hard-to-fill jobs and opened small businesses in the empty storefronts of struggling towns. As a generation of non-Hispanic white children leaves for college and seldom returns, immigrants are keeping many of those communities alive.