I have seen musicians play on stage while barefoot. It depends on the venue as to whether that is appropriate or not. If you are in a classy music venue (Grand Ole Opry, Bluebird Cafe, Red Clay Music Foundry, etc.) or in a restaurant - the dress code might preclude going openly barefoot. But if it's a laid back outdoor concert at a music festival, there may not be a dress code (depending on the festival clothes might be optional).
Whether barefoot or not, a concert stage has many hazards that a musician must be aware of. I personally like to minimize trip hazards and keep the stage floor as tidy as possible. I bundle my cords and run them in an area that keeps the main stage free of clutter. Obviously your instrument cable and mic cable can't be tied to the front edge of the stage but most other cables can.
I certainly want to be sure that no electrical cords or cables are in use that could create an electrical hazard - whether playing barefoot or not.
You might want to try one of the minimalist running shoes or barefoot shoes such as the ones pictured below. These would offer some protection from splinters or hot surfaces or environmental hazards (germs, chemicals) while allowing better feel of your pedals. Unlike socks they have a sole that is resistant to tearing and absorption of liquids and dirt. These shoes would qualify as "shoes" in a venue such as a restaurant where the local health codes might require all patrons and occupants to wear shoes and shirt.
Image of EvoSkins from Wikipedia article on minimalist running
Image from www.kensavage.com
Rugs have been mentioned and those are a great idea whether barefoot or not. A rug on stage protects your instrument and mic cables from the hard surface of the stage should you accidentally step on one. Instead of a rug, what I use is an EVA foam (rubber) mat made to go under exercise equipment or on gym floors. They roll up for transport and come in 4' x 6' or in 8 foot lengths and diminish fatigue of standing on stage. I actually have several and put my floor monitors on one in addition to placing one under foot to stand on. Compared to a rug, these mats offer more cushion, are lighter weight and easy to clean if a drink gets spilled on them. Mine are dark grey (almost black). They lay flat on their own but with mic stands and guitar stands on the edges, they don't go anywhere.