Unfortunately, though "no shoes no shirt no service is NOT a government regulated law. Nor is it an across the board thing every establishment has their OWN views on what is acceptable and what is not. It is also NOT associated with ANY health regulations.
No shirt/shoes/service signs rules that SOME (stressing the word SOME) businesses choose to display to help steer away, "unsightly" or impoverished would be customers, to help keep the place looking "nice" and "respectable". They are NOT health regulations, nor are they required to turn away service from individuals without certain items of clothing.
If it were a health hazard, for public places to have people running around without shoes, then health departments across the country would be shutting down tanning salons, nail shops, and beaches, like wildfire.
I hate to tell you, but not having on shoes, is NOT a health hazard. Neither is not wearing a shirt. Feet, are no more dirty than hands, and if your THAT worried about germs, being transmitted via uncovered body parts, Id be more worried about that nail tech that didn't wash her hands after they came in direct contact with her booty after she went to the bathroom and didn't wash her hands, than a pair of feet that have been covered and protected by layers of cotton and rubber all day. (And while they may smell a little they are probably not as big of a health threat as unwashed hands laden with hep.B)
ya know?