GREENSBORO, N.C.—The wall behind the bar at Jake’s Billiards has 69 taps offering beer choices that range from California’s Lagunitas Fusion 22 to Natty Greene’s Buckshot, which is brewed across town. The last tap in the long row belongs to Budweiser, and it is about to be removed.

A Halloween promotion earned Budweiser a place at the bar, a hot spot frequented by students and recent graduates of the University of North Carolina here, but owner Jessica Dewey sees no reason to keep Bud on tap. She sells 20 cases of Bud bottles...