First, thanks for an informative essay.
People do seem to have an intuitive sense that justice--how people should treat one another--involves some form of mutual respect: taking one another into account as we live our separate lives together in this world. 'Real justice' distinguishes justice from morality. The former follows from the observation that we humans have no choice but to effect choices, whereas the latter is always bound up in immaterial beliefs
if curious: "Real Justice, and the Living's Easy" (here in Medium but not behind the paywall)