Self-hood is not just a characteristic of persons, but things--even if it is illusory. You were at pains to identify with one tradition (ie Eastern) and dis-identify with the other--one the path of liberation, the other of confusion, etc. The world is a lot more complicated than that. People practicing Christian traditions frequently gain clear understandings of suffering, emptiness, luminosity, etc. And there are people with no understanding of such things who accomplish a lot of good in the world. (Among them are people on this list.) And, of course, there are people who do understand such things who are schmucks. And then, there are Native American traditions, and Wicca, etc. Are they Eastern? Western? Deluded? Enlightened?
In other words, the response you suggest to political left and right--has x let go of the self?--threatens to become a kind of primitive theism. It's a litmus test of virtue or enlightenment, or something that is supposed to have clear meaning politically, but doesn't. Besides, it's not a political answer--foreign policy dilemmas and budget problems will not be solved if enough people see through the illusion of the self, however good that would be in other ways. Having a common experience of non-selfhood might provide a good ground to begin with, but conflict doesn't end there. Politics is a different order of (non) reason. But that's why bodhisattvas practice the paramita of exertion :).
Christian