Unfortunately the "left-right" divide is at the very crux of figuring out what "justice" and "living a good life" actually mean, so we can't bypass politics and go straight to "making things better" until we agree on what "better" means.
Briefly, left-wing folks think that it's best when everybody is equal, right-libertarians think it's best when everybody is free, and the Catholic Church and other religious types think it's best when everybody does what God says.
Yeah, but it's insane to construct left-right divisions into issues like social justice and cooking! Basic human rights (social justice is a synonym of those) are universal.
Check some definitions:
"Fair and proper administration of laws conforming to the natural law that all persons, irrespective of ethnic origin, gender, possessions, race, religion, etc., are to be treated equally and without prejudice. See also civil rights."
http://www.businessdictionary.com/definition/social-justice....
Briefly, left-wing folks think that it's best when everybody is equal, right-libertarians think it's best when everybody is free, and the Catholic Church and other religious types think it's best when everybody does what God says.