> But how does a modern, complex and non-homogeneous society aribiter cases without turning "poisonous" or odious to some members?
There is no perfect society in this regard. Just because it's hard doesn't mean that such societies shouldn't strive to reduce the odiousness, and maximize the fairness in the administration of justice, regardless of the subgroup that the contending parties may belong to. Fair and equal treatment under the eyes of the law is a cornerstone of human rights.
> To my knowledge much of Europe, M.E., Asia and even S. America are composed of largely homogeneous populaces with a smattering of outsiders at best.
You've listed regions that contain some of the most heterogenous countries on earth in ethnicity, language, and culture, like the UK, France, China, India, Iraq, Lebanon, Indonesia, Brazil.
Some of these countries have multiple, sometimes contradictory legal systems, some sanctioned by the state, others by religious power structures.
The country that is often referred to as among the most homogeneous societies in the world, Japan, has a pretty well acknowledged dual justice system for citizens versus visitors. All societies fail at this, but if anything, the very homogeneous societies fail the most at offering equal justice.