Moral intuitions and cultural relativism

When I teach introduction to ethics I spend some time on cultural relativism. I present several objections to the view, mostly based on counterintuitive consequences involving certain moral behaviors, such as criticizing one's own society's moral code. I've noticed that in the context of discussions of cultural relativism, students become hesitant to trust their own moral intuitions. "Who are we to say," they say.

But this hesitation completely disappears the next day when we move on to discussion of utilitarianism. I present standard criticisms of this view, most of which are based on the idea that it misclassifies certain actions--it classifies certain wrong actions as right or obligatory. Now the students are unhesitating. "Yeah, you absolutely can't perform the organ harvest. No way," they say.

Although I realize this is not scientific, I guess I think it's pretty weird. Maybe contemplating cultural relativism gets people in a more tolerant mood. But the harms contained in the counterexamples to utilitarianism (organ harvesting; free-riding; etc.) pale in comparison to the harms we discuss in connection with relativism (Jim Crow; slavery; the holocaust; etc.). Maybe just introducing the prospect of relativism primes them to regard morality as relative. Does this happen to other people?

--Mr. Zero