Not everyone who is racist has had a traumatic experience. I think it's nice to rationalize that she has an underlying reason for it, but I think it would be cheap if there were. People who are prejudiced usually don't have a good reason for it. I don't think it's infeasible that Nina has simply been raised by people who scorn or fear the Elevens. Milly's family doesn't strike me as exactly model Britannian citizens - they wouldn't have helped Nunnally and Lelouch if they were, I suspect.