In Japan, being invited to a person's home is a high honor and you remove your shoes at the door, only to slide into provided slippers to wear while in the home. In addition, you must change those slippers and put on “toilet slippers” if you should need to visit the Powder Room, but remember to change back into the “house slippers.”
My classmate from Shanghai comes to visit me in Oklahoma City and immediately removes her shoes and wears little foot hose in my house. Some people are cognizant of the environment and do not want to track in pollution and chemicals as well as dirt.
So knowing which one of these areas is the cause will be helpful to you in your decision regarding how to handle this situation. Etiquette is about everyone feeling comfortable around each other. So I see you have a few options:
1. Wear or take socks or slippers and put them on when you enter the house so you are not barefoot.
2. Ask to meet at a professional location such as an office or restaurant to discuss business.
3. View it like this — it is his house, it is a business call and when doing business in another's country, you should follow their customs or requirements. This is proper protocol, but required to be barefoot is not.
4. If he wants you to go barefoot, get another new person to work with!