Is there a law about no shirt no shoes no service?

Those signs became popular in reaction to "hippies" and teenagers in the 1970s. The rule was subsequently adopted by many boards of health especially in businesses where food is served. You would need to check in your particular jurisdiction to determine the status of the rule in your area. There is no universal law since health regulations are usually set by local jurisdictions.

Wearing shoes can also be a requirement for insurance purposes since injuries to bare feet are more likely in a retail establishment and victims may sue for damages. In many cases it is simply the choice of the business owner who impose that rule out of consideration for other customers who find shirtless, shoeless people to be distasteful. Any business management can post such signs as long as they are enforced consistently.