No, going barefoot is actually quite legal for customers and violates no health regulations.1 Individual businesses may set their own rules regarding patrons and bare feet, but government regulations do not address it. A restaurant cannot be fined for the actions of their patrons, only for their employees' conduct. There are many health departments or regulatory agencies that require shoes for certain workers, however, so check with them for specific guidelines.

1. "Bare Feet and the Health Department," Society for Barefoot Living (Link)