I was generally staying out of this even though I think you're dead wrong in this discussion, but if you are saying "stats" is how prejudiced opinions are formed, that is one of the most ill formed opinions I've yet to read. It's true that statistics can be bent, but so can any branch of science. To ignore general trends is to ignore reality. Of COURSE there are differences within any group and those differences can be described in any number of ways; including using the word "nuanced". No one is saying people within any group are homogenous, but if you don't think people receive differential treatment based on gender, race, etc. and that this doesn't tend to have an effect on how they view the world, you're dreamin...
Leaving "generalities" out of a discussion of something like voting that, almost by definition, speaks to generalities is, well, silly. What you define as nuance, looks awfully close to a bell curve. WHY those nuances exist is another matter.