I wouldn't remove my shoes in a client's home. It's funny how they don't mind hair all over their carpet/floor, but not a pair of shoes? Besides, what if i dropped something such as scissors/something heavy and got stabbed in the foot/broken foot?
I think I would either tell all new clients when they booked, before i went to their home, or I'd carry a small pair of indoor shoes with me. If they still didn't allow me to wear those, I'd refuse to cut the hair.
Just my opinion.
Kams xx