I've always found it silly that you could take a magical set of clothes and change its appearance into something radically different-looking and expect it to have the same properties afterwards. Not to mention, some people have, um, "peculiar" choices when they change them, too.
So yeah, certain items cannot be changed. You can't make a Miko Dress look like a suit, or dye a Black Cloak neon green. This only pertains to magic items found in loot. Crafted items and generic clothing bought in stores can be altered to your heart's delight.