He's pointing out the contradiction people hold in their heads, not saying that it's immoral. Many people believe in mutually incompatible ideas like this. I think it's because they get more satisfaction from fitting in with the crowd or experiencing the pleasure of reinforcing their beliefs than they do from trying to be right, which is emotionally unrewarding.

I think they should be honest and say "It's OK to discriminate against people based on the circumstances of their birth but I make an exception for race because my society told me I must." It sounds kind of stupid, but it is stupid. That's the cost of honesty.