If you read internet discussions about the subject of the shoes-off rule, you will find countless people who claim to have a medical condition that means they must wear shoes all the time. If these discussions were representative of the population; nearly half the people in the USA have such a medical condition. I do not believe a word of it.
Yes, there are some people who do have a genuine medical reason for not removing their shoes. We must make exceptions for them.
Some people say having a shoes-off policy causes embarassment for such people because they must reveal their condition. However, this is quite unnecessary. A person with a medical condition can simply say:
I am sorry, I can't take my shoes off. Doctor's orders.
She does not need to reveal the nature of her condition. She does not need to give any embarassing details. There is really no problem here.