Seems to me that under the normal understandings of social justice and truth, that real social justice requires truth.
Social justice requires no more truth than striving for injustice. Whether an outcome is social justice or injustice is purely a matter of subjective emotion and feeling, and not a matter of objective truth. If a personal preference for how things should be is met, then its "justice", if not, then its "injustice".
Social justice is no more related to truth than a goal like making as much money as possible. While there are truths about what methods will best achieve the goal, the best methods often entail telling and spreading untruths about various things to get people to act in ways that achieve the desire goal.
Achieving social justice means getting people (and the systems they control) to act in a particular way that produces particular "just" outcomes. Very often, telling lies is more effective than telling truths at getting people to act is those ways. Thus, social justice goals, no matter what ideological values are the basis for determining those goals, will almost never be best served by sticking to truths. Rather, some truths will serve the goal, some truths will be neutral, and some truths will impede the goal. Note that none of this means that the goals are wrong in a moral sense because moral wrongs have little to do with factual truths.
Take any "social justice" goal of any political camp and there will be countless ways in which bending, hiding, or denying various truths makes achieving that goal more likely. There is only one goal for which this is not the case, and that is the goal of only supporting the objective rational truth about everything.
So, any academic that is striving for any political, social, or justice goal will necessarily have motive to violate the principles of rational thought and discourse that are the foundation of any respectable academic discipline.
Basically, it is the same reason why profit motive is not generally compatible with basic science. Objective truths and those truth being known to all is only occasionally going to be the best path to the most profit.