"What makes a man go neutral? Lust for gold? Power? Or were you just born with a heart full of neutrality?" -- "Captain Zapp Brannigan," Futurama
There is a considerable body of philosophical argumentation pro and con ethical relativism. However, I harbor the suspicion that the argumentation is irrelevant to what makes people ethical relativists or anti-relativists. (We lack a really satisfactory term for whatever the denial of relativism is. "Realism" has the wrong connotation for non-philosophers. "What's so 'realistic' about your view? Relativism seems more 'realistic' to me!" I think "realism" also lends itself to the mistaken impression that to be an anti-relativist you have to be a Platonist. "Objectivism" would be just the right term, except that it has been appropriated by Randians, that cult of pseudo-philosophers.) Anyway, back to the main topic. If philosophical argumentation has little effect on one's belief in relativism or realism, what does?
When I get into an extended discussion of this issue, it becomes clear to me that ethical relativists generally think that relativism is a more open-minded view. Realism, they think, is the view of people who are judgmental and narrow-minded. Realists, on the other hand, seem to think that relativists are morally wishy-washy. "How can you really believe that Nazism is wrong if you're a relativist? And if you don't really believe Nazism is wrong, how will you oppose it?"
When pressed, my experience has been that philosophical realists and relativists will back down from these commitments ... at least nominally. (The realist will admit, "Well, I suppose you do oppose Hitler, in your own subjective way." The relativist will say, "Okay, I guess you could be an open-minded realist.") But I've had the odd experience of arguing with someone, having them admit that there is no connection between, say, realism and dogmatism, and then listening to them bring that claim up later in the same conversation as an explicit or implicit assumption.
I once read an unpublished study that attempted to establish an empirical connection between a commitment to ethical relativism and open-mindedness. There were a lot of methodological problems with the study, though. For one, the author noted a correlation between flexibility in solving mathematical problems and a tendency to believe ethical relativism, and tried to draw the conclusion from that. However, just because someone is flexible, creative, and "open minded" in mathematical contexts, that does not entail that he or she is ethically open minded. (William Shockley, one of the inventors of the transistor, was a notorious racist and advocate of race-based eugenics.) Nonetheless, I think it is interesting that the author of the study was using as his working hypothesis the claim that ethical relativists would be more open-minded.
My own experience has been that people who advocate most loudly for ethical relativism are generally not open-minded. Indeed, in my years of teaching, relativist students have been positively rabid in rejecting anything that challenges their views.
What about the claim that realists tend to be dogmatic? My experience has been that if people continually employ the rhetoric of "facts," "evidence," and "proof" in discussion, they are generally extremely dogmatic. Troubled actor Dustin Diamond ("Screech" from the show Saved by the Bell) was on a weight-loss reality show where he informed his doctor that his views could not be refuted because they were based on the unshakeable power of rational proof: among Screech's "rational" beliefs were that he did not need to eat less or exercise more to lose weight. Maybe it is the "proof" part that is the root of the trouble. "Proof" is a weasel word in philosophy, which typically confuses more than it illuminates. There is really no proof outside of mathematics and formal logic, and some would argue that we do not find absolute certainty even there. In any case, I don't find most realists to be dogmatic. Then again, I might be subject to confirmation bias, since, like most people, I find it easier to sympathize with people I agree with.
Perhaps we need to approach the issue more pragmatically. Maybe we should simply focus on the vices that are really bothering us (dogmatism and apathy) and try to avoid them.