Moral relativism is an unpopular philosophical position, at least within academic philosophy departments, and there are a couple of obvious reasons for this.
One is its association with a truly crazy idea, espistemic relativism (or truth relativism) - the idea that truth about the universe is not objective, but exists only relative to cultures or perhaps even individuals. This is a self-defeating idea, because someone who propounds it need not be listened to, even according to her own advice. The obvious rejoinder is, "Well, truth is objective in my (or my culture's) worldview. Go away!" If the idea is modified to something like, "All truths are relative except this one," it raises the question of what is so special about this particular truth. May there not be other truths that have whatever mysterious property grants objectivity in some cases? Furthermore, espistemic relativism, taken literally, denies the objective truth of seemingly undeniable facts about ordinary experience ("There is a computer in this room, but no hippopotamus."). And it flies in the face of science's success in understanding the world. An epistemic relativist will typically say (and is logically committed to) such nutty claims as that there is no objective truth to the heliocentric model - rather than a geocentric model - of our solar system. The craziness goes beyond science, narrowly defined: for example, we are left with the conclusion that there is no objective answer to whether or not atrocities such as the Holocaust actually took place.
Another reason for the unpopularity of moral relativism with philosophers, apart from its association with the crazy idea of espistemic relativism, is that it is typically advanced in a very naive form which includes a crude argument about how moral relativism entails a requirement for tolerance of other cultures. This crude argument can easily be demolished, but that then destroys the psychological attractiveness of the theory for many people.
I suppose a third reason may be this: taken seriously, moral relativism is a challenging doctrine. It requires us to say that there is a sense in which seemingly incontrovertible moral claims are false. No one wants to be stuck with denying the objective truth of a claim such as, "Hitler's actions in attempting to exterminate the Jews were morally wrong." That makes the doctrine psychologically unattractive, to say the least, just as its supposed connection to cultural tolerance may make it attractive to many.
In fact, moral relativism does have something going for it in terms of delivering a more tolerant, less fanatical, morality than do traditional, commonsense, moral ideas. It is just that the effect is somewhat more subtle, and the arguments somewhat more complex, than those which are usually offered and which I have seen demolished repeatedly by philosophers as diverse as Bernard Williams and Peter Singer. David Wong and Neil Levy have explored the issue in much more depth than can be seen in the sort of vulgar relativism that is commonly picked up by undergraduates before philosophy teachers go to work on them.
There is, indeed, something unsettling about the claim that moral propositions, including those that condemn evil actions such as those adding up to the Holocaust, are not objectively true. It is far more comfortable to be able to condemn such actions without complex explanations or secret caveats. However, comfort does not equate to truth. It is actually quite easy to make me feel uncomfortable about positions that I am convinced are true but go against my socialisation (for which reason, I am a good philosopher but would make a lousy politician).
I'm convinced that a rational being (perhaps from some distant planet) that refuses to condemn the Holocaust is not necessarily making an intellectual error, provided that the normative judgment it makes is consistent with its own most fundamental values and it makes no mistakes of empirical fact or of reasoning. While it is objectively true when I say that, "The Holocaust is condemned within my own system of norms, which I consider justified," it is not true that I can necessarily find an error in the reasoning or the knowledge base of any rational being that refuses to make such a claim. If such a being proceeds to act towards us in much the same way that Hitler acted towards the Jews, we may consider it to be evil, but that does not entail that it is making an intellectual mistake.
My claims in the last paragraph are a crude, perhaps distorted, summary of the views of Gilbert Harman; whether or not Harman would accept the way I have formulated them, they seem to me to be correct. At the same time, they are remote from the usual kinds of vulgar relativism. They are still slightly uncomfortable ideas to try on for size, because they are not consistent with widespread and commonsense metaethical beliefs or with the wish to be able to condemn Hitler unequivocally. In so far as they claim that widespread and commonsense metaethical beliefs are false, these ideas amount to an error theory of morality, though Harman himself has attempted to develop them in a way that avoids this implication (my provisional view is that he does not succeed, but I don't think much depends on this).
There is a limited sense in which we cannot condemn Hitler unequivocally: i.e., we can imagine him taking the same actions even if he had not made many intellectual mistakes, e.g. about human biology. However, in the end, I'm not too worried about not being able to condemn Hitler in that sense. The worst thing about Hitler was not his actual intellectual errors, but other features of the man - his malevolence, cruelty, fanaticism, and so on. For most human beings, fortunately, these are qualities to which we are fiercely opposed. Our opposition is based on very deep values that are widely shared among us. We have very powerful reasons to join together in expressing our horror at Hitler's actions and in resolute opposition to the Hitlers of the world. In such extreme cases, the fact that Hitler can be imagined to have acted as he did without making intellectual errors does not water down the vehemence of our response.
However, in cases where less is at stake, theories (such as moral relativism) that deny the objective truth of moral claims may lead to our watering down some moral responses. Where the values involved are not so deep and widely held, we may come to see some moral norms as more like the norms of social convention, to which we may be attached, but not whole-heartedly. This sort of watering down of at least our less deeply and widely held moral beliefs is very unwelcome to moral conservatives, but I actually think it is something that should be welcomed.
Sophisticated non-objectivist theories, such as those of Gilbert Harman and John Mackie are not as immediately attractive as vulgar moral relativism, but they have the great virtue that something like them is actually true (and this is an objective statement about the universe!). Furthermore, by a more subtle route they can deliver what is (for many of us) admirable about the more vulgar kinds of moral relativism, without the extreme of preventing us from condemning Hitler (or even more everyday murderers and rapists, and the commonplace cruel or callous people with which the world is well-stocked). While these theories require careful explanation, and are not straightforward to grasp, they should resonate with philosophy undergraduates and other educated people who are currently working with relativist ideas of a less sophisticated kind. They are onto something, even if they cannot articulate it in the careful manner of somebody like Harman.
This suggests to me that philosophy teachers should be less trigger-happy about simply shooting down vulgar moral relativism, and more willing to explore the implications of non-objectivist accounts of morality, to see where they lead when refined. I also think that moral philosophers should be more prepared, in their own work, to explore the normative implications of such ideas; like some of the other thinkers I've mentioned, particularly Wong, I think that rational and sophisticated non-objectivist metaethical theories do have normative implications. In particular, they can preserve our full horror at grossly violent or cruel acts, while leading us to a less rigid morality when it comes to actions more at the periphery of our moral thinking. Overall, I think this is beneficial (though that is itself a value judgment that can be disagreed with by somebody who is not necessarily making an intellectual error).
In short, I'm calling for an approach to moral philosophy that may not have much resonance for most current moral philosophers (though I see a few signs that non-objectivist theories are making a comeback), but may have a lot of quite justifiable resonance for our students and within the larger culture. This resonance will give its prescriptions a degree of political realism, even if they are not popular with philosophers. The approach I am calling for fits well with a naturalistic account of the universe and ourselves, and, most importantly, has truth on its side.