It doesn't bother me at all. I think lots of the mixed-breed yorkies are really cute, have good temperments, and might possibly have some good traits our purebreds don't have-like being more easily potty trained, for example!
I admit, I have asked a couple people if their dogs were purebred/if they were yorkies before-but not because I was turning my nose up at all. Yorkies come in so many sizes, colors, and "looks" that sometimes it's hard to tell, and I'm truly interested in what breed their dogs are. We had a neighbor that had a silky-but looked very much yorkie, only bigger. I also ran into a lady at Petco that had a dog that looked like a yorkie, only it was really curly-but it was purebred. She too thought it was a yorkie-poo when she got him, but found out that he was indeed purebred. I had never heard of a chocolate yorkie or a biewer until I got on here-and I definitely would have asked those owners about their dogs' breeds too
But, I think it's all in how you present it and ask the question.