States and municipalities have long used financial incentives to lure new businesses. But when taxpayer-funded incentives benefit a new rival, existing local businesses can get angry.

Consider the resentment stirred up in Richmond, Va. The city on the banks of the James River, with a population of about 200,000, has a burgeoning local dining and beer-brewing scene, touted as a draw for tourists. Now Richmond itself intends to get in on the craft-beer boom, through an incentive package offered to Stone Brewing Co. of Escondido,...