Well there's plenty of Millie-type names that get flung about on here the whole time which aren't derided for not being 'proper' names.
In fact, a common refrain is: 'Why call her Catherine for the birth certificate if you're going to call her Katie? Just call her Katie, it's fine!'
It's got fuck all to do with it being an abbreviation. It's because it sounds black and working class to bigoted ears.