I have in mind any form of moral realism that just meets the definition, but it is not a form of what Street calls “realism about normativity”—e.g., see her paper “REPLY TO COPP: NATURALISM, NORMATIVITY, AND THE VARIETIES OF REALISM WORTH WORRYING ABOUT” (I do not agree with calling that “realism about normativity”, but that is another matter)-
But the paper in question does outline a distinction clearly enough for this context I hope; in particular, she says “I have concluded that Copp’s view is not normative realist in the sense targeted by the Darwinian Dilemma.”. Now, I do not think Copp’s view is correct, either, but the point is that there are kinds of realism not targeted by the Darwinian Dilemma (DD). Granted, Street goes on to say that the kinds of realism not targeted fail to “vindicate moral requirements as objectively binding.” I would say that while I do not think ‘objectively binding’ is the right term (as in somehow suggests that not having that is a failure of some sort), what she describes as ‘objectively binding’ seems to be non-existent—but that is still not a problem for moral realism as defined above (and in the other thread).
Now, Street correctly points out that many leading moral realist philosophers do defend a kind of realism that the DD targets, and I would agree that that form does not exist. But I do not think this is a problem for realism, again in the sense described above, which I think is also the sense that is defined in the other thread (though as I mentioned, there is some ambiguity in the definition therein).
For example, reading the arguments in Street’s papers (see for example, “Objectivity and Truth: You’d Better Rethink It”, or the reply to Copp), one can say that any version of moral realism that is not committed to the claim that immoral behavior is necessarily irrational, is not targeted (it is not even considered a form of realism by Street, but it is by the definition in the other thread, at least as I think is property interpreted).
In my assessment, there are morally wrong behaviors, and whether a behavior is immoral is a matter of fact, but while immoral (i.e., morally wrong, unethical, etc.; those are synonyms) behavior is nearly always irrational, it is not always so (probably not even in the actual world). The DD isn’t even targeting any view with those properties