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The high school basketball squad from Eagle Grove, population 3,700, had traveled 60 miles up Highway 69 in Iowa to play the team from Forest City, population 4,100. It would be the Eagles against the Indians, a hardwood competition in the center of the country. For some people, this is as American as it gets.

At one point during the online streaming of the game last month, two white announcers for a Forest City radio station, KIOW, began riffing on the Hispanic names of some players from the mildly more diverse community of Eagle Grove. “They’re all foreigners,” said Orin Harris, a longtime announcer; his partner, Holly Jane Kusserow-Smidt, a board operator at the station who was also a third-grade teacher, answered: “Exactly.”

For some people, this is as American as it gets.

Mr. Harris then uttered a term occasionally used these days as a racially charged taunt, or as a braying assertion that the country is being taken back from forces that threaten it. That term is, simply, the surname of the sitting American president.