Vampirism basically makes their fur white right? This is just personal perspective but maybe it's a case of Marie Antoinette syndrome - becoming a vampire, dying and undying, is probably very taxing and stressful on the physical body. So much that it damages the hair/fur follicles or something. But the issue with that is human hair, as mentioned already, so..yeah.
It's probably just a gameplay decision so you can distinguish a khajiit vampire more easily, maybe?