A Latino grocery on the west coast of Central Florida, El Mariachi Loco, has been celebrated for two decades in the local media as a symbol of the region’s growth and diversifying population. Its homemade tacos and sopes left one reviewer feeling “wonderful to be alive.”

Then last week, was hammered with criticism about stale bread, poor customer service and an invasion of roaches. But the complaints weren’t due to an actual infestation or rancid food at the Sarasota, Fla., business. It was because a Donald Trump yard sign...