My Orpington has had the same dirty butt problem since she was old enough to grow feathers, so it might be a different cause, but I had her droppings tested by vet and no parasites. She is active, eats well, and otherwise looks healthy so I have given up worrying. I just put her in the shower every few weeks. I use a hand held sprayer with tepid water and brush her feathers with a soft toothbrush to knock off dingleberries. Then I wrap her gently in a towel and hold her for a few minutes to dry. I don't use soap, but there probably is some way to do that. This hen is very tame and sits still during her showers, so it's easier than washing my dogs!
i have recently started to put a teaspoon of cider vinegar per gallon in their water thinking it might be a digestive situation, but no change yet.