ARCADIA, Wis.—Small towns in the Midwest have diversified more quickly than almost any part of the U.S. since the start of an immigration wave at the beginning of this century. The resulting cultural changes appear to be moving the political needle.

A Wall Street Journal analysis of census data shows that counties in a distinct cluster of Midwestern states—Iowa, Indiana, Wisconsin, Illinois and Minnesota—saw among the fastest influxes of nonwhite residents of anywhere in the U.S. between 2000 and 2015. Hundreds of cities long...