While reading the SEP article on empirical approaches to moral psychology I came across the discussion of criticisms of moral realism related to Mackie's 'argument from relativity,' a.k.a., 'argument from difference', which is basically that the existence of fundamental moral disagreement undermines any claim that moral judgments are objectively true. In particular the argument discusses one variation on this, namely, that moral realism should imply that moral views converge through protracted argument, which they do not, therefore, etc.
But, of course, tha tricky point with this argument is that no other realism is committed to such an absurd claim. For instance, realism about evolution is not committed to the claim that protracted argument will lead to convergence on belief in the occurrence of evolution; evolutionary realists are not refuted by the existence of anti-evolutionists. And this is a much stronger opposition than we usually get in the case of moral disagreement, where the differences, although undeniably real and stubborn, tend to be much more subtle -- a difference of emphases. An example the authors of the article give that is supposed to be a problem for the realist is the tendency of those raised in southern states to have stronger physiological reactions to perceived affronts than those raised in northern states. But this is a pretty weak sort of opposition on which to base an anti-realist argument; it's as if you said an experiment suggesting that people from cities and those from farms notice different things in their environment would constitute evidence against the existence of the external world. Or, rather, from a moral realist perspective the parallel would be reasonably strong, although not perfect.
As moral realists have noted, convergence is not an issue unless the convergence in question is an idealization of an approximation over the long term; and it's a much harder sell to argue that there has been no such convergence on any moral point, e.g., the evil of slavery. Indeed, as I've pointed out before, the UNICEF charter, and the Universal Declaration of Human Rights following it, are based on such a convergence: while people disagreed about the right sort of arguments to use to justify certain rights, it was clear that they could often agree on particular rights. The interpretations of those rights would not be exactly the same across different cultures, but, again, the variation is far from being a rigorous opposition. And this is, I take it, the mistake the authors are making: assuming that variation is a sign of non-convergence, which is straightforwardly false. To use a physical analogy, if you and I are converging on a point that we won't, at our present trajectories, reach before the week is out, the fact that we are not in the same place at the end of the first day is not evidence against the claim that we are converging. (For that matter, if at the end of the week we are not standing on exactly the same place, but instead are right next to each other, this is not evidence against convergence, either.) Convergence is a process; in the case of ideas, when we are dealing with such a large population as the human race, it is a complicated and sometimes extremely long term one. Even in clearly factual matters, human beings do not all converge directly and immediately on the same facts, the mere fact of variation tells us nothing at all about whether they are converging or not, and even if it did, it wouldn't be enough, because what's relevant is whether they are able to converge rationally. (One of the problematic assumptions of the article is that realists would have to 'explain away' diversity; when in fact all realists of any field need is an explanation of how convergence is possible, which basically comes down to the questio of how we know moral truths. Attacking this point would be a far stronger argument against moral realism than the mere fact that people have various opinions on moral matters, and certainly a better argument than the fact that people have different physiological reactions in the same situation.)
The point is not a minor one, for what's really being attacked here is the potential for social progress, and the denial of such progress has serious consequences. After all, social progress is simply convergence on a better position; and even moral anti-realists don't usually want to deny that in moral terms the repudiation of slavery has been convergence on a better position, even if they disagree with moral realists about what 'in moral terms', or even 'better', implies.