LEON BRIDGES doesn’t wear hats anymore. “It gives me away so quick,” said the 28-year-old singer. When Mr. Bridges emerged on the music scene in 2015 with his debut album “Coming Home,” he was often seen in a Stetson fedora. He wore one in publicity photos, on stage and in the pages of GQ, becoming known for the pinched-crown hats—too known for his liking. Today, the musician prefers to go hatless, but his style still snags attention.
Mr. Bridges’s debut album, Southern soul at its finest, sounded like it had been dug out...