Because you're right: we are, all of us on DU, privileged in that we don't live in a place where things like this happen. These people live in a world where hacking your neighbors to death has become normalized, because as you point out, the hatred is passed from one generation to the next. Each group views the others not as people, but as enemies. The prevalence and strength of the cultural hatred has resulted in the dehumanization of the "others" to the point that hacking them to death with machetes and burning their homes is just what one does. And if they don't do it first, then the others will do it to them, because it's happened before.
We can't imagine living in that world. The poorest of us have privileges and resources that these people can't imagine. We live in a society where violence is proscribed and it's accepted that one doesn't physically attack or kill others, regardless of how strongly one disagrees with them. When someone does display that kind of remorseless brutality in our culture, it's not uncommon that they actually are psychopathic.
To us, the mindset of "hack a different group to death with machetes" is psychopathic, not in a clinical sense but in a shorthand sense. It's a quick way to rationalize events like these, rather than a literal psychiatric diagnosis. This mindset is so outside our frame of reference that "psychopathy" is a label we can put on the behavior in order to understand it from our point of view.
I don't think any moral relativism was intended, and I don't think Muriel was exercising privilege. I think that, in a moment of shock and revulsion, she used a term to describe the behavior in the only way she could think of at that moment.