Is it essential to do martial arts (like: Karate, Kung Fu....etc) in bare foot?

I would say most schools would allow wearing shoes. Not just your every day wearing shoes though. You might have to buy certain shoes that can only be worn on the mats, not to be used outside to dirty the mats up. I also think wearing your shoes or everyday clothes should be what you train in. Reason I think is when you are on the streets you don't wear a gi or go bare footed.