READING, Pa.—Joseph Nuñez at first didn’t like Donald Trump. “I couldn’t stand the guy. I didn’t like the way he spoke about Hispanics or people in general,” he said. But by 2020, Mr. Nuñez had become a fan of Mr. Trump’s style and priorities, and he voted in favor of giving the president a second term. So did many other Latino voters in this working-class city who had once backed Democrats or, like Mr. Nuñez, had skipped elections altogether. Now, as political strategists continue to sift through the 2020 election results, the emergence of these newly Republican voters is setting...