FYI I don't think your view matches Pratchett's intention (which of course doesn't make you wrong). At one point Vimes (I think) asks Carrot about this, and Carrot replies that having dwarves for parents has never been a dwarfish definition of being a dwarf.

Ultimately the sensitivity of these question comes from the fear of hidden inferences--the concern that when you say Carrot is not a dwarf, you're implying that it's wrong for him to observe dwarfish customs. I suppose you have the equal and opposite worry, that once we start calling Carrot a dwarf we'll build him a house with four-foot ceilings?

Another job for taboo.