Saying "I am not prejudiced, but" then Making a Prejudiced Remark Means You Are Prejudiced

I know that what I am about to say has been said before, but I think that there are people who do not seem to grasp the concept. Saying "I am not racist (or homophobic or sexist or prejudices, etc.), but" before making a racist comment is not very convincing. Many times the person is about to make a racist, homophobic or sexist remark. They often refer to statistics to justify a prejudiced point of  view. Statistics can be manipulated to justify almost any point of view. The same kind of "logic" was used by the Nazi party in Germany. If you have to preface something with the above mentioned phrase it might be better to reconsider what you are about to say. Saying you are not prejudiced then making a prejudiced does not make sense. It just means that you are in denial about being prejudiced.