Since the cultural turn of the 1970s, liberals have focused on cultural change as a way of achieving justice. They assumed that people conform to dominant social norms which they learn about through the media and through others in society. So the operating hypothesis is that, if you create the impression that (for example) racial equality is the dominant social norm through consistent and uniform expression of those views and the suppression of racist norms, then racism will disappear as people start to conform to those new values. (This is in contrast to the prior Marxist-influenced social science which assumed that culture mainly reflects economic realities, and you can't make racism just disappear while keeping the same economic conditions.)
Jonathan Haidt is a social psychologist and one of the co-authors of the paper. His work theorizes five foundations of morality—basically, ways of assessing the moral value of an act: harm, fairness, respect for authority, loyalty to one's group and purity/sanctity. The impact of the cultural turn shows up in his research. He found that conservatives tend to use all five foundations, while liberals only use the first two. Obviously for liberals, the remaining three are associated with patriarchal authority, nationalism and religious oppression.
So, he's not just demanding equal representation of political ideologies. It seems that Haidt believes that the dominance of liberalism among social psychologists is harmful to the field because it is associated with a strategy of cultural change which obliges liberals to avoid lines of research into these other foundations of morality.