I guess occasionally someone wants to talk about the crime rate or income disparities between races and wants to throw in some caveats before they wade into a touchy subject, but anyone sensitive enough to discuss something that nuanced usually isn't going to toss out their entire viewpoint in half a sentence (the half after "I'm not a racist"). Anyone able to talk about a complex hot-button issue in an appropriate way has better and more specific caveats than the shitty old "I'm not a racist," which is apparently a good marker for illiteracy as well as racism.
By the way, the above screenshots come courtesy of I'm Not Racist, But ..., which is one of several blogs that track this phrase across the Internet, showing that despite how well-known and mocked it is, you still can't swing a dead LOLcat without hitting an "I'm not a racist but" tweet or comment.