I think that the 'sorting' is done in the same order you see when you actually try to dye something. There are "whites" in the far-right dye set choice (and purples, and golds, etc), which is what I see in the 'sorted' order above. Of note is that there are the normal dyes (in order), followed by the green-background dyes, followed by the 'purchasable' dyes in green-background.