Butter. Sap is not water soluble, so soap and water won’t work. It is, however, fat-soluble, so you must rub an oil (any pet-safe/food oil will work) into the fur and incorporate the two together. Then you can use soap and water to rinse out the mixture. Voila! Works like a charm on many hydrophobic substances.
Blueberries and other vaccinium species do well with a wood mulch top layer as they make fungal associations that help them deal with environmental stress. It also help retain moisture.