I'm a mutt of about 6 different European nations plus Taiwanese, but it really depends on which side of the race card they are pulling:
I say I have Romani heritage, and people always think that *all* "Gypsies" are crooks, murderers and bums. Nope, some people just fell off the bandwagon and it does get under my skin a bit.
Why is my last name Williams? It's because apparently Casimir Witkowska is too hard to pronounce when my family came to the US in the 1910s and was treated like an outcast, so my great-grandpa became Allen Williams, not because my family owned slaves (I have gotten that once from someone who thought too much, since there seems to be more Black Williams people than Caucasian I guess).
Chinese? I'm Taiwanese. Here's where I admit I'm a bit prejudiced; there are certain mannerisms and about China I don't approve of (such as uncontrolled gross pollution, plagiarism, willful disregard of human life), not to mention Communism destroyed my family and they were refugees that fled to Taiwan, so I'm actually deeply ashamed of Chinese heritage just like how some Germans are ashamed of their 3rd Reich (which I'm also part German and despise Hitler, but verdammt, everything else about Deutschland is so fucking awesome).
Any other facet (British, Italian, Scottish, Irish)? I take it with a grain of salt... Or a glass of Guinness
But still, for the things I don't approve of with, they will
definitely know. I usually say something right then and there but usually matching the tonality and context of how they said it, but anything further I do confide in a higher-up.
Conversely, I usually try not to say anything about other races; maybe Chinese lifestyle, mannerisms and politics, but I very seldom crucify anyone just for being Chinese alone... But my ancestry traces back to them so I can get away with it