Just to cross the beams of pedantry here for a moment, a widespread and well known --- if less than serious or systemic --- cultural/social bias against red haired people, probably first coming into public consciousness in North America due to the infamous South Park 'Ginger' episode, has in fact primed you to select "redheads" as a non-contentious example of a plausibly ethnic group that might be discriminated against, something that every red-haired person knows, although you apparently do not. This means that the choice is statistically insensitive and the social methodology is poor.

Actually, choosing an identifiable group at random would be both socially and statistically unwise, as, following Patero distribution, there are vastly more minority/extreme minority distinguishable groups of people than there are majority/significant minority ones; this means, firstly, that any group randomly selected with equal biasing between all groups has a high probability of being subject to actual discrimination, mooting any social benefit of choosing a group at random; secondly, that the generalizable qualities of the group chosen would therefore have a distribution with very little deviation (if I'm using my terms correctly) and would be highly predictable, thereby obviating any possible statistical benefit of doing so.