It depends, I suppose, on how you define the term “racist.”
To some people, a racist is somebody who treats people differently based on what race they are. This is what I would call the “classic” definition and the one held by the majority of people. I personally strive to treat everybody the same way, regardless of their race, and would therefore consider myself to not be a racist under this definition.
To others people, however, a racist is somebody who refuses to acknowledge racial differences and tries to treat everybody the same way (e.g., “you’re not respecting my black culture, so you must be a racist.”) This is what I would call the “post-modern” or “backlash” definition. After years of insisting that they be treated equally, some minorites now bristle at the thought and want to be treated differently (albeit in a way of their choosing and not as dictated by the majority). Since, as mentioned above, I personally strive to treat everybody the same way, regardless of their race, I might be considered racist under this definition. My willingness to treat somebody as they want to be treated extends only so far, and there are definitely days when I get tired of treating somebody differently just because they feel they deserve special treatment.
Finally, to other people, being a racist means believing that there are, in fact, different “races” and not accepting the “fact” that race is nothing more than a social construct (i.e., to even talk about different races makes you, ipso facto, a racist). I’d almost call this a non-argument, since it really amounts to redefining the terms of an argument instead of actually proposing a solution (claiming that there really is no such thing as a “black” person doesn’t help the thousands of apparently imaginary black people who are discriminated against everyday regardless of their imaginary status), but I know that there are a lot of people who sincerely feel this way and it should not be dismissed out of hand. However, since I feel it is more beneficial to argue that racial differences are insignificant when it comes to determining personality or character, rather than argue that there are so such things as racial differences in the first place, I suppose I would also be considered racist under this definition.
I think education can definitely help people become less racist, at least with reference to the first definition described above. Much of that type of racism is, I believe, the result of upbringing and small sample size (if your parents tell you that blacks are stupid, and the one black you met was, in fact, stupid, you just might be led to believe that all blacks are, in fact, stupid). A decent education can help in many ways. First of all, it can develop critical reasoning skills that allow one to distinguish the fallacy involved in making broad generalizations. Second of all, it exposes one – either directly or through literature – to a much wider sample of humanity than one might experience otherwise. Third of all, hi Opal! (sorry, I’ve been wanting to do that for awhile. I promise it won’t happen again.)
I’m not sure whether a good education can really help with the second definition of racist. Theoretically, I suppose it’s possible to become so knowledgable about every possible culture that you always know exactly how to treat members of every minority you meet, but the problem with that is that some indivduals want special treatment as a member of their minority, whereas others genuinely want to “blend in” with the majority and would rather be treated as if they were a member of that majority. That means you either have to be a mind-reader or else risk offending somebody the first time you meet them until you can determine how they would like to be treated.
As for the third definition of racist, I really have no idea whether education can help or not. Nor, for that matter, whether becoming “less racist” in reference to this definition is actually a worthwhile proposition in the first place. As I mentioned earlier, I think society is better served by acknowledging racial differences and educating people to understand that these differences are literally only “skin deep,” rather than denying the common sense evidence of racial identity all together.
But then, that’s just me…

Barry