When Representative Troy Nehls of Texas voted last year to reject Donald J. Trump’s electoral defeat, many of his constituents back home in Fort Bend County were thrilled.

Like the former president, they have been unhappy with the changes unfolding around them. Crime and sprawl from Houston, the big city next door, have been spilling over into their once bucolic towns. (“Build a wall,” Mr. Nehls likes to say, and make Houston pay.) The county in recent years has become one of the nation’s most diverse, where the former white majority has fallen to just 30 percent of the population.

Don Demel, a 61-year-old salesman who turned out last month to pick up a signed copy of a book by Mr. Nehls about the supposedly stolen election, said his parents had raised him “colorblind.” But the reason for the discontent was clear: Other white people in Fort Bend “did not like certain people coming here,” he said. “It’s race. They are old-school.”

A shrinking white share of the population is a hallmark of the congressional districts held by the House Republicans who voted to challenge Mr. Trump’s defeat, a New York Times analysis found — a pattern political scientists say shows how white fear of losing status shaped the movement to keep him in power.