Basically, the question is how telling somebody something is "racist" (or sexist, or anti-Semitic, or whatever) impacts their subsequent expressions on racial issues. This interests me, because (assuming that most Americans don't like thinking of themselves or being thought of as racist) one can imagine two very distinct response types.
One hypothesis is that people will moderate their previously held views, or otherwise act in a more minority-friendly manner following the charge. This theory flows somewhat out of (is kind of the reverse, actually) the idea of "moral credentialing". The moral credentialing literature establishes that when people act in a friendly manner towards an outgroup, they gain a "credit" which they can cash-in later to justify subsequent unfriendly acts without damaging their self-image as non-prejudiced. It would stand to reason that calling someone "racist" might create in their minds a moral "deficit", which they would then try to settle by engaging in subsequent friendly acts (so I'll call this the "deficit reduction" hypothesis).
Another hypothesis is that people will "double down" on these views, or otherwise act in a more minority-hostile manner following the charge (the "double down" hypothesis). Once again, we start from the premise that the charge of racism is disturbing to their self-image. But under this hypothesis, this results in either (a) a need to deny the charge and not take actions which seem to implicitly concede the charge is legitimate (which altering one's view might do) and/or (b) increased hostility towards the person rendering the charge, resulting in greater antipathy towards that group (this would presumably vary based on the identity of the person making the charge).
In my experience, I've seen both. Certainly, the premise behind the first hypothesis is pretty deeply inlaid in the entire structure of anti-racist practice: that "calling out" things as racist shames perpetrators and alters their behavior for the better. But the alternate hypothesis I've observed as well -- some people seem to respond even more aggressively when they feel like they are being called racist for taking certain positions. Some seem to revel in this -- they genuinely seem to enjoy "tweaking" their critics -- but for others it seems considerably more defensive and better explained by a desire to preserve their self-image as non-prejudiced.
I envision two separate experiments (the methodology is tentative -- I don't really know methodology). I also envision doing some survey work to help subdivide participants into, for example, "high-prejudice" and "low-prejudice" -- I gather this is something that is regularly done in these sorts of studies and there are established practices):
(1) A subject is asked to give their opinion on a racially-salient topic (say, affirmative action). When they are finished, a researcher tells them that they believe that what they said is racist (it doesn't matter what they actually said). Then they are taken to a different room, with a different researcher, and asked the same question. Their answers to the first and second questions will be coded to see if they become more extreme, less extreme, or stay the same.We would thus be measuring the "double down" effect in two ways. The first study would be more directly political and is thus open to the possibility that the person strongly feels that their original position is pro-minority. The second study resolves that by removing the subjectivity in what decision is pro-minority. It relies on the well-established literature that prejudice manifests in situations of ambiguity.
(2) The study begins exactly the same way, with the researcher telling the person that they believe their response is racist. In the second part of the study, however, the participant will be given a non-political opportunity to render assistance to a minority in an ambiguous situation (or select between similarly-qualified minority and non-minority candidates for a mock job position).
I make two intersecting predictions. First, I predict that low-prejudice persons will generally be more inclined to engage in deficit-reduction, and high-prejudice persons will generally be more inclined to engage in doubling down. The non-racist self-image of the latter group is more precarious and thus more threatened by assertions of racism. Moreover, the hostility they feel towards the charge will reinforce their extant negative feelings towards the charger. Meanwhile low-prejudiced persons, because they are more secure in their egalitarian self-image, will paradoxically be more willing to contemplate that their views might need to be altered in response to critiques from minority perspectives.
Second, I predict you will see more doubling down across the board in the first experiment compared to the second. This plays off (but somewhat inverts) the observations of ambiguity. Altering one's views after being told one's prior views were racist relatively unambiguously communicates at least a partial concession that the charge was true and legitimate, which people will be reticent to admit. By contrast, the second study does not overtly communicate any message that the subject is recanting their prior beliefs, and thus allows for a restoration of a non-racist self-image without any implied concession that they were previously acting in a racist manner.