Oh, carts are filthy. (I'd recommend against letting your kids ride in them, btw, as I know someone who works at a Stop and Shop, and they use the carts for their garbage and discarded raw chicken containers..)
Still kind of annoys me when one thing bothers people for being dirty, and they take pains to avoid/sanitize that one thing, when the fact is we're basically living in filth up to our elbows all the time, and usually manage to survive.