The No Shirt No Shoes policy is just a policy and not a law.
The store or business owner has the right to refuse service to anyone who does not wear a shirt or shoes.
It's not a health department thing but just a store policy that they put in place.
Even little kids in a shopping cart have to wear shoes.
I once tried taking my 2 year old son into the store in just a diaper and shirt because I had changed his diaper in the car because he leaked out of his diaper and go pee on his shorts.
So I left his shoes off and his wet shorts and put him in a new diaper and put him in the shopping cart seat.
I walked up to the store and they said I had to put his shoes on to bring him in the store even though he was in the shopping cart.
So I had to go back out and get his shoes and then they let him and me in.