liability for bare feet
Venues can comfortably allow barefoot patrons and protect themselves from legal issues by keeping floors reasonably clean and giving simple notification that hazards to bare feet may exist.
One common misconception about people going barefoot in public is that stores, restaurants, libraries and other venues will be liable if the unshod patron is hurt. We've looked extensively into this legal issue and can say that venues, with a little knowledge, have nothing to fear from allowing patrons without shoes.
Without getting too technical legally, establishments have a "duty of care" to patrons whom they invite in. These venues should make a reasonable effort to get rid of dangers that might cause harm but must -- at a legal minimum -- warn patrons of any potential dangers. A perfect real-world example of this is with wet floors. When a liquid spill happens, staff should make a reasonable effort to clean it up and they must warn that a hazard exists -- and usually do this with "Wet Floor" signs.
Establishments are not legally responsible for the actions of their patrons. When someone walks into a public venue, they legally assume whatever risk they bring upon themselves.
If a grocery store customer chooses to walk on a recently-mopped surface that is displaying a "Wet Floor" sign, the law sees them as taking on the liability for that risk. If a patron goes barefoot in a venue and have been made aware that hazards to bare feet may exist, they are making the decision to assume the legal risk of injury if footwear would have otherwise protected their feet. An example of this is if they know broken glass may be on the floor, stay barefoot anyway, and cut their foot.
A venue's management who are concerned about their liability for a barefoot patron should make a resonable effort to keep the floors clean and need only inform the person that there may be hazards around that can injure their feet. This can be done verbally in front of a witness, or by posting signs at public entrances that read, "Hazards to uncovered feet may be present." That notification fulfills the establishment's legal duty of care to those visitors.
related: facts about safety when barefoot