There are NO federal or state laws in the U.S. that specifically and directly ban bare feet in public. There are only about a dozen (12) local laws directly prohibiting bare feet among the 20,000 ordinance-passing cities, and those few laws address only specific locations like a particular park or arena.

Some states, provinces and local governments do require by law that patrons of specific businesses obey posted warnings and directions. If those warnings and directions indicate that footwear is required, then bare feet are indirectly prohibited by law. For example, the State of Missouri Statute RSMO 316.230 requires that riders obey all warnings and directions regarding all rides at amusement parks.  Failure to comply may lead to ejection from an amusement park and is a state misdemeanor.1

That said, state law may protect some barefooters if a business has no established, posted policy. In those cases, a business cannot just make up a dress code on a whim.

There's actually one county in the State of North Carolina that has an ordinance2 protecting bare feet outdoors. It actually prohibits persons from depositing on sidewalks or streets anything "likely to injure barefoot persons."

For more information on laws that apply to barefooters, contact your state, province, or local government's law enforcement agencies.

1. Worlds of Fun Website, Frequently Asked Questions (Link)
2. The Solid Waste Management Code of Buncombe County, N.C., section 62-30(d)(4).