You can't permanently dye fur, but maybe you could mod the follicle to grow into a tattoo. Also, for certain fur colors and types, (Especially white) tattooing the skin beneath the fur would allow it to be visible.I wonder how tattoos would work with furred/feathered/scaled players, of if they would be flat out unavailable. Verusha has tattoos, after all. Maybe, if they're implemented someday, players with furred/feathered skin would pay a lot more, since the dying would be more expensive. I think that goo or latex-skinned players should have them unavaliable, due the nature of their skin surface.
All of this, is speaking hypotetically, if they make it into the game.