Then I'd want to know how that absolute morality, and the relation between it and minds, fits into that person's overall ontology. To say that moral realism is incompatible with atheism, if atheism is just defined as not-theism, is a stronger claim than to say that it's incompatible with the kind of reductive materialism that Dawkins espouses. Dawkins himself seems to agree that his worldview won't support moral realism.

Of course, it's possible to respond by saying that moral realism is false. But then I wish people who think this wouldn't intermittently make comments which seem to presuppose that moral realism is actually true, e.g. by saying that there are things which, morally, we should or shouldn't do, or comparing their moral views with those of other people in a way which suggests some standard external to both.