Social justice is not a subset or different kind of justice, rather it is a particular theory of what justice is. It generally holds that equality and fairness are important principles that must be factored in to determining what is just as opposed to simply focusing exclusively on liberty and property rights. If you're familiar with the debate between John Rawls and Robert Nozick, then you could say that Rawls's position is more in line with the views of those who advocate for social justice, whereas Nozick advocated for libertarian justice.

OP's post is a bit naive and misplaced because s/he suggest that those who do not believe in social justice are opposed to justice itself. This is incorrect, however. Those who do not care for social justice simply have a different conception of what justice is.

The real problem with discussing social justice in a law forum is that the concerns raised by those interested in social justice are typically consider matters of policy, that should be handled by legislatures, rather than legal issues related to the administration of justice, that should be handled by courts. Only in the limited sphere of constitutional law do any of these substantive questions related to justice get settled by judges as opposed to legislators. Even in that context, law serves primarily to limit legislative actions that might be unjust, but it does not set affirmative policy goals, which is primarily what social justice calls for. Of course, lawyers as people and citizens should care about social justice, but that doesn't really have much to do with them being lawyers. Law, as a profession and academic field, is really about administration and not so much about policy.

OP may also be confused about the particular phenomenon on reddit and other internet forums of criticizing so called Social Justice Warriors (SJWs). That criticism stems from a disdain for political correctness and certain brands of feminism and other anti-racist or pro-egalitarian positions. Essentially, those who criticize SJWs embrace a particular form of right-wing propaganda in an effort to discredit and silence those who they perceive as bleeding heart liberals. The phenomenon is all over the internet, and OP is within his/her rights to feel indignant about it, but that's not an issue with law or legal culture, rather it's a problem with internet culture and contemporary politics.