Universalist stereotyping. Everybody stereotypes their own people as well as outgroups.

From The Moral Stereotypes of Liberals and Conservatives: Exaggeration of Differences across the Political Spectrum by Jesse Graham, Brian A. Nosek, and Jonathan Haidt. They are working off the Moral Foundations theory.

From the abstract:

We investigated the moral stereotypes political liberals and conservatives have of themselves and each other. In reality, liberals endorse the individual-focused moral concerns of compassion and fairness more than conservatives do, and conservatives endorse the group-focused moral concerns of ingroup loyalty, respect for authorities and traditions, and physical/spiritual purity more than liberals do. 2,212 U.S. participants filled out the Moral Foundations Questionnaire with their own answers, or as a typical liberal or conservative would answer. Across the political spectrum, moral stereotypes about “typical” liberals and conservatives correctly reflected the direction of actual differences in foundation endorsement but exaggerated the magnitude of these differences. Contrary to common theories of stereotyping, the moral stereotypes were not simple underestimations of the political outgroup's morality. Both liberals and conservatives exaggerated the ideological extremity of moral concerns for the ingroup as well as the outgroup. Liberals were least accurate about both groups.

The discussion at the end of the paper is a little clearer.

Results indicate that people at all points on the political spectrum are at least intuitively aware of the actual differences in moral concerns between liberals and conservatives: they correctly predicted that liberals would care more than conservatives about the two individualizing foundations and that conservatives would care more than liberals about the three binding foundations. The results also confirm previous studies of partisan misperception by showing that, in general, people overestimate how dramatically liberals and conservatives differ. Remarkably, people even morally stereotype their own ingroup, with liberals overestimating liberals' strong individualizing concerns and underestimating liberals' weak binding concerns, and conservatives exaggerating conservatives' moral concerns in the opposite directions.

Our results go beyond previous studies, however, in finding and explaining an otherwise puzzling result: liberals were the least accurate. We presented three competing hypotheses about accuracy: 1) We found some support for the hypothesis that moderates would be most accurate, which they were in the case of the binding foundations. However, and most crucially, partisan inaccuracies were not mirror images of each other (in which case the red and blue lines in Figure 2 would have opposite slopes). On the contrary, liberals and conservatives both tended to exaggerate their binding foundation differences by underestimating the typical liberal and overestimating the typical conservative. 2) We found no support for the hypothesis that liberals would be most accurate; liberals were the least accurate about conservatives and about liberals. The largest inaccuracies were in liberals' underestimations of conservatives' Harm and Fairness concerns, and liberals further exaggerated the political differences by overestimating their own such concerns. 3) Finally, we found some support for the hypothesis that conservatives would be the most accurate, which they were in the case of the individualizing foundations. In line with Moral Foundations Theory, liberals dramatically underestimated the Harm and Fairness concerns of conservatives. These findings add to the literature on moral foundations by demonstrating a novel form of pragmatic validity for the theory: conceptualizing and measuring the moral stereotypes people have of different social groups.

While we obtained a nationally-representative sample for comparison of MFQ scores, it is important to note that the predicted answers as typical liberals/conservatives all came from a non-representative Project Implicit sample. However, the participants in this study do “run the gamut” across the ideological spectrum, from very liberal to very conservative, and Figure 3 demonstrates exaggeration across all 7 points on the political orientation item. Extreme liberals exaggerated the moral political differences the most, and moderate conservatives did so the least.

[snip]

The ideological “culture war” in the U.S. is, in part, an honest disagreement about ends (moral values that each side wants to advance), as well as an honest disagreement about means (laws and policies) to advance those ends. But our findings suggest that there is an additional process at work: partisans on each side exaggerate the degree to which the other side pursues moral ends that are different from their own. Much of this exaggeration comes from each side underestimating the degree to which the other side shares its own values. But some of it comes, unexpectedly, from overestimating the degree to which “typical” members of one's own side endorse its values.

[snip]

It is striking that instead of basic partisan outgroup derogation, in which both sides predict that the other is less moral in general, we found foundation-specific moral stereotypes about liberals and conservatives—and these moral stereotypes were largely shared by all. Participants across the political spectrum exaggerated liberal moral disregard for Ingroup, Authority, and Purity, and conservative disregard for Harm and Fairness—that is, exaggerations of the patterns predicted by Moral Foundations Theory. This suggests that moral stereotypes might be unique in that they are motivated (partisans want to cast the other side as immoral) and yet partisans share the same moral stereotypes about either side. Even more surprising, they share both of these moral stereotypes with moderates, who are presumably not as motivated to stereotype either side.

[snip]

In this study, we focused on the moral values of ideological opponents, and their perceptions of the moral values of either side, in order to understand the moral “distrust and animosity” endemic to the liberal-conservative culture war. We found that there are real moral differences between liberals and conservatives, but people across the political spectrum exaggerate the magnitude of these differences and in so doing create opposing moral stereotypes that are shared by all. Calling attention to this unique form of stereotyping, and to the fact that liberal and conservative moral values are less polarized than most people think, could be effective ways of reducing the distrust and animosity of current ideological divisions.