No one has "unwarranted" prejudice. There is no such thing as "uninformed" bigotry. Those who have prejudice and bigotry, have very valid reasons in their own mind, for the sentiment, or they wouldn't have it. Ask any prejudiced bigot why they feel that way, and they will explain with clarity, why they hold the view they hold. Ignorant bigotry, doesn't mean someone is stupid, quite the contrary, they are usually very smart. Their "ignorance" comes in not realizing their own bigoted and prejudiced views for what they are.
As humans, we are all born with prejudice. People exhibit prejudices everyday, in what they eat, what they wear, the friends they have, the places they go, the car they drive, the neighborhood they live in, etc. This is normal human behavior, but our politically correct social culture has so vilified the word, that people are ashamed to readily admit they have prejudice of any kind. I happen to think this is the single biggest obstacle to defeating racial and sexual prejudice which is prevalent in our society.
If people of all races, and people of all gender and sexuality, could realize and understand, we are all inherently prejudiced, and it's normal... we might be able to better understand each other. We all have things we prefer and things we don't prefer, and there isn't anything wrong with that, we are human. These simple preferences are often misconstrued into "racial prejudice" or "sexual prejudice" when they really aren't anything more than common human behavioral traits.
It is only when these common traits translate or manifest themselves into discriminatory prejudice against individuals based on stereotypes supported in our prejudices, that we have a fundamental societal problem. Realizing and understanding, each person is an individual creature, with their own set of prejudices as well, and we are all part of a larger group working together to form a society, is the key to understanding and tolerance. Respect for each individual, their unique attributes and character, irrespective of their race or sexual orientation, is the key to combating discriminatory prejudice.
As a society, we need to realize, we can never completely eliminate all prejudice and bigotry, in fact, it is a bigoted view to think that we can. You can't change other people, only yourself. In that regard, we should avoid hypersensitive emotive reaction to anything we personally perceive as prejudice, as when someone is called "racist" because of some innocent comment they make. From my perspective, this detracts from the problem of real racism, which does exist. We should reserve that word to apply it justly to those who indeed hold the view of racial supremacy or inferiority. If we focused our attention on those cases, we could effectively change hearts and minds.