This is the situation that most people in the United States seem to feel uncomfortable about. This turns out to be a complete myth . At the following website are letters obtained from the Health Departments of about 40 American states confirming the non-existence of any such regulations. No Service This, of course, is not referencing any law, ordinance or statue.
Most trouble appears to come from chain coffee-shop type restaurants.
If you are confronted, the thing to do, is to remain calm and to remember that you are the customer. On the other hand, you may just want to go elsewhere. Over time, you will build up a collection of eating places that aren't uptight over you or your kids being barefoot. A few people say that they don't want to see feet while they are eating. This is an interesting, but entirely nonsensical neurosis.