The reasons why some store owners don't permit bare feet can be summarized as:
Lack of understanding.
Belief that there is a health department regulation.
Belief that they open themselves up to liability in case of injury.
Belief that bare feet are "offensive to other customers."
The detailed answer to this question has been superceded by the
A Case for Bare Feet paper, specifically section 2:
Discrimination.
The paper is available on-line at:
Is it legal to
Which stores do