It's an unrealistic expectation and you can't accommodate it. If it is that concerning to them let them find a "clean" daycare.

Years ago I was a Girl Guide leader with the 5&6 yr olds. There was a mom that had a 5yr old in my group (and an 8yr old brother) the house rule was the kids couldn't bring paper home. All art work was tossed in the trash can as they left our meetings. Same for school art work. It all went in the trash immediately as mom didn't like paper cluttering the house.

At age 5 this girl had already learned to not put any effort or enjoyment into our art projects because it was thrown out. It was sad. It was an unrealistic rule to put on children.

Kids get dirty, kids should LOVE getting dirty and a dirty child is indeed a badge of honor of a good childcare group. Of course there are always those kids that can't handle getting dirty but it needs to the child that doesn't like it not the parent.