Mr. Huckins and his wife, Ginger, were leaving Portland, Ore., one of the most progressive cities in the United States. They said Portland’s tolerance of homeless encampments, along with the open use of hard drugs and rising crime, had filled them with despair. So they headed 2,000 miles east, to deep-red rural Missouri.

Driving around their new hometown in June, about an hour outside St. Louis, they admired the old Victorians and a tractor defying the minimum speed limit on a state road.

“One thing I do like about Missouri, there’s lots of American flags,” Mr. Huckins said as he steered around a traffic circle where the Stars and Stripes flapped crisply on a pole. “In Portland, the American flag was offensive.”

One day earlier, in a neighboring state, another couple making a politically motivated move had a different flag on display — a Pride flag on a T-shirt.

Jennie and Jeff Noble were packing their possessions into a 26-foot U-Haul truck in suburban Iowa. Ms. Noble, 37, who was wearing the Pride T-shirt, and her husband were leaving Iowa for Minnesota.

Their only child, Julien, came out as transgender at age 11. Now 16, Julien uses prescription testosterone. After Iowa banned gender-affirming medical care for minors, criminalizing their son’s treatments, the Nobles — lifelong Iowans — concluded they had to get out.