The challenge for the moral subjectivist is to give a meaningful account of what MLK was up to. If morality is subjective, why should anyone ever go against the the status quo? Moreover, the subjectivist cannot say that MLK brought about a better state of affairs through his efforts. All the subjectivist can say is that MLK brought about another type of morality that is just as legitimate as the one he replaced. This is problematic for two reasons: (1) it is obvious that the morality MLK introduced is, in fact, better than the one he denounced; (2) if MLK was just introducing another equally viable ethic, he should be called immoral for going against the accepted morality of his culture.
Unfortunately, I don't think subjectivism is so easily refuted. Clearly one could go against the status quo for the sake of personal/subjective values. MLK didn't like racism, so he fought against it. Simple. Moreover, the subjectivist can say that the resultant state of affairs was indeed better according to MLK's values - and, of course, our own. So there's nothing problematic about the fact that most of us prefer the obtaining of a less racist state of affairs.
The only serious restriction subjectivism poses here is that we cannot say that this result is better for everyone, or just 'better' simpliciter. But - arguably - neither of those statements would be true anyway. The first is clearly false: some individuals (e.g. racists) are surely worse off now than they used to be. The second, one might argue, is technically meaningless: value judgments must be made relative to some set of interests or preferences, so there is no 'better', simpliciter. The universe doesn't care about racism. Only people do. (That's the grain of truth hidden within in the otherwise pernicious doctrine I play at defending in this post.)
So JD's talk of equally 'legitimate' rival moralities may be taken as nonsensical by the subjectivist. "Equally legimate from whose viewpoint?", the subjectivist could ask. From within our perspective, racism is simply wrong, and any suggestion to the contrary is mistaken. We don't consider the racist's views to be legitimate. They are to him, within his viewpoint, but that's not one that we need approve of. Objectively speaking, there just isn't any fact of the matter independent of these rival perspectives. One might say it is the viewpoints themselves that are equally legitimate, rather than the substantive moralities they in turn endorse. But they're not 'equally legitimate' in any positive sense - for there's no standard against which to make such a judgment - instead, they're simply incommensurable.
As for the 'going against his culture' objection, subjectivists (unlike cultural relativists) would deny that the dominant culture is privileged in any way. MLK was wrong according to the racists, but right according to himself (and us). There's nothing more to be said about the matter, according to subjectivists. We certainly shouldn't call him "immoral", for we share his values! But yes, racists could do so (and probably did).
The very idea of progress in morality presupposes an objective standard against which these changes can be evaluated. The alternative is to say that no morality is better or worse than another (i.e., there is no objective standard), which belittles the work of great moral reformers like Martin Luther King Jr.
Although I'm sympathetic towards these sentiments, a subjectivist could plausibly disagree. Clearly objective progress is impossible according to subjectivist/relativist accounts, but one can still assess changes according to how well they comport with one's own subjective preferences. We think MLK is great. He changed the political landscape in a way that we all consider favourably. The subjectivist would say there's nothing belittling about this. Cosmic approval being not ours to bestow, the greatest honour we can give someone is our personal approval, and MLK receives precisely that.
P.S. I'm actually not a subjectivist. Indeed, moral relativism quite often infuriates me. My next post will balance this one by explaining why...