Social justice makes sense in light of the emergence of collective guilt as a social regulator and a certain idea of privilege associated with it. The dynamics is as follows:
Group A is privileged relative to Group BThe idea of social justice necessarily emerges out of the emergence of collective guilt as a social regulator. It is no coincidence that the idea of social justice was developed by Marxist Catholic theologians. It is a different kind of thing from what one typically associates with "justice" when it is associated with either guilt cultures or responsibility cultures. These tend to be more individualistic in nature, even if there can be a collective component to some notions of justice within guilt culture.
The world is a zero sum game
Therefore, what Group A has was necessarily taken from Group B
Therefore, Group A should feel guilty about their privilege
And, equally, therefore, Group B deserves social justice from Group A
The difference is that in guilt cultures, "our" group is just, but your group that threatens our law/principles is necessarily unjust. Keep in mind that the Inquisition was a court system designed to hand out justice. Within responsibility cultures, justice is always necessarily individualistic. You are responsible for your actions; others are not responsible for who you are and what you do; justice is thus related to your actions and your actions alone.
With the idea of collective guilt, you can actually make the argument that your own group is guilty and that therefore justice is owed other groups. It is still group-think and fundamentally tribalistic, but what is gone is the idea that one's own tribe is necessarily and by definition good while others' are bad. By breaking down the us-good/you-bad dichotomy (or, all too often, reversing it), one can develop the idea that other groups are being treated unfairly as groups by other groups as groups. Those groups which are being treated unjustly need some sort of reparation for the injustices they have suffered, while those engaging in the injustices ought to feel guilty, as a group, about those injustices.
But how does a group perpetuate injustice against another group? Through institutions. Now, it is certainly true that there are institutions within pretty much any given society/culture which privilege one group over another. Often by design (Jim Crow laws, minimum wages, anti-drug laws, etc.). While many who promote social justice argue in favor of redistribution, another option is institutional reform and/or the creation of new institutions. There is certainly something to be said about the kinds of criticism which arise out of the idea of social justice. This is why there are even libertarian arguments for social justice. But of course, the solutions are typically going to be different in nature.
Thus we can see that social justice is in fact a coherent idea. One just have to understand it in relation to the right social regulator. As a part of collective guilt culture, it makes perfect sense, even if it appears to be utter nonsense to responsibility cultures, guilt cultures, or shame cultures. Naturally, for those who are regulated by naturalistic principles, social justice is hardly nonsense, even if it is something which, through institutional reform, we can hope to move well beyond.