Asked visitors to wash their hands before holding our 2 month old. My uncle took it personally

Since the naming ceremony there has been a steady stream of relatives coming to see our daughter, most evenings. My partner and I agreed on one rule: wash your hands before you pick her up. Most people are fine with it. My uncle was not. He said he had raised three children without anyone sending him to the sink, and he left early. Now my mother says I embarrassed the family. I don't want to drop the rule, but I would like to keep it without a scene every time. What worked with the older relatives in your family?