Some subjects, to counter in-group loyalty, overcompensate by demonstrating out-group loyalty. Uhlmann, E.L., Pizarro, D.A., & Bloom, P. (2008):
Additional suggestive evidence for awareness of automatic attitudes comes from work showing that implicit and explicit measures interact to predict judgments and behaviors. These interactions suggest that people not only compensate, but
in some cases even overcompensate for their automatic attitudes. For example, individuals who are automatically prejudiced but who are consciously motivated to respond without prejudice respond even more favorably towards Black targets in terms of their trait judgments (Olson & Fazio, 2004) and willingness to interact with the person (Towles-Schwen & Fazio, 2003) than individuals who are not automatically prejudiced (see also Dasgupta, 2004). As noted earlier, increased awareness of an automatic process can lead to correction effects (Newman & Uleman, 1990; Moskowitz & Roman, 1992).
In terms of Haidt’s dimensions, this phenomenon probably arises from the fairness dimension, from considerations about historical injustices to minorities. It’s probably not a direct inversion of the in-group loyalty dimension.