May states choose only certain types of businesses to be closed on Sundays?
Yes. Where the state determines that a day of rest would be desirable in some kinds of businesses and not in others, they are permitted to restrict only those that they deem to be necessary. Likewise, the state may decide to forbid or limit the sale of certain items (such as alcohol) on any given day, so long as the decision is justified by some secular purpose instead of a religious one. In a 1999 decision, Harris County, Texas v. CarMax Auto Superstores, Inc., the 5th U.S. Circuit Court of Appeals upheld a Texas law that forbade car dealerships from being open on consecutive Saturdays and Sundays. Effectively this forced the business owners to choose one day or the other as a day of rest for their employees, though it did not dictate any particular preference as to which one should be adopted. The court denied that the law unfairly discriminated against car dealers or established any sort of preference for religion as opposed to no religion.
