The main reason people apply social justice concepts to climate change is that a) the right defected from their initial agreement to fix the problem with carbon

The main reason people apply social justice concepts to climate change is that a) the right defected from their initial agreement to fix the problem with carbon taxes and other market mechanisms, then b) spread a lot of propaganda about how addressing the problem was going to hurt the poor. So anyone who wanted a democratic coalition to deal with climate change had to look to the left of the political spectrum for support and dispel the notion that it would make the poor poorer.