Dwarves have been common in Ankh-Morpork for about... 20, 30 years? (For fans, I'm going by the time difference of Night Watch and Thud! Night Watch takes place about 20-30 years ago, when dwarves are rare, and Thud! shows them firmly set in Ankh-Morpork.)
Plus, it would be decidedly Pratchett-esque for an immigrant to assimilate so thoroughly that he became anti-foreigner. Dwarves have a streak of xenophobia in them to begin with, so it's not too crazy to think that one of the dwarf characters could be anti-foreigner.