I think my answer to the question would depend on the kind of "hurt" involved. I think it'd be more personally insulting to be called a liar, but it would be more socially and professionally harmful to have a reputation as a racist. Although I was offended many years ago online when a woman made a comment to me like "I bet you think I should abort my racially-mixed child" and I was like wtf I've never said anything even close to that before, but that was also because I thought I was on reasonable speaking terms with that person. But I guess if it's a person that I have no connection with, I couldn't care less what they think of me.
Anecdotally I know several people that have reputations for being dishonest, but they get a pass for various reasons, such as simply having already been a friend. I've never met a person in real life with a reputation for being actually racist. Closest thing would be a Filipino guy that could get away with talking about how he doesn't let his little sister play with black boys, and cracking racial slur puns, but he would even do it in front of the lab with black friends/peers around, so it's obvious that even if he was 100% joking and non-racist, there is a gap between being racist and being perceived as a racist.
There might also be a geographical component; reputation of being honest might be more important in a smaller-town environment than in a large city, and likewise I could imagine that in a racially homogeneous town, no one really gives a fuck if you're racist because it isn't relevant. Overall I don't think sociological surveys, particularly where self-reporting and self-identity are concerned, are worth much to begin with.