With bigotry, I think the real problem is confirmation bias. If I believe, for example, that orange-eyed people have an average IQ of only 99, and that's true, then when I talk to orange-eyed people, that belief will prime me to notice more of their faults. This would cause me to systematically underestimate the intelligence of orange-eyed people I met, probably by much more than 1 IQ point. This is especially likely because I get to observe eye color from a distance, before I have any real evidence to go on.
In fact, for the priming effect, in most people the magnitude of the real statistical correlation doesn't matter at all. Hence the resistance to acknowledging even tiny, well-proven differences between races and genders: they produce differences in perception that are not necessarily on the same order of magnitude as the differences in reality.
Those are real and important effects (that should probably have been included in the original post).
A problem with avoiding knowledge that could lead you to discriminate is that it makes it hard to judge some situations - did James Watson, Larry Summers and Stephanie Grace deserve a public shaming?
A few examples (in approximately increasing order of controversy):
If you proceed anyway...