One of the reasons that racism is so difficult to eradicate is that many people genuinely feel less empathy for members of other races. The insidious thing is that they may not even be aware that they feel this way.
If they don't know they have these feelings, then how do we know they do? One way is by using Implicit Association Tests (IAT). These tests ask people to sort words or images into groups as quickly as they can. For example, a volunteer might have to decide whether to put a lemon in the ‘good’ or ‘bad’ category. People are much quicker at sorting things in a way that makes sense to them. A racist might put a dark-skinned face in the ‘good’ column for the benefit of observers, but he’ll be a lot slower about it than a person who really believes dark-skinned people are good.
Sure enough, even people who don't consider themselves bigoted and who make every effort to act and speak in unbiased ways often display inherent prejudices when subjected to these kinds of tests.
Maister, L., Sebanz, N., Knoblich, G., & Tsakiris, M. (2013). Experiencing ownership over a dark-skinned body reduces implicit racial bias Cognition, 128 (2), 170-178 DOI: 10.1016/j.cognition.2013.04.002.