As an "other ethnic" myself, I reckon that the best thing to do is learn to take the p!ss out of yourself before anyone else has the chance. That way it not only takes away ammunition from people but also means that you get used to laughing at such comments when they are meant as slurs - nothing annoys the bigot more than when you laugh at their "finest riposte"!
Edited to add that I've never experienced any serious attempt at racial abuse during my 11 years in.