Well, I think a lot of indigenous groups in America and Africa did in fact have cultures that granted very little power to the State. But those groups were mostly not agricultural, and so they had low population density and very limited military defenses, and were largely overwhelmed by the military force of absolutist monarchies and then republics during the colonial era. (There were also agricultural indigenous cultures overwhelmed by colonization in both America and Africa, but those cultures also had high degrees of social stratification and state power, at least in the examples I'm familiar with.)
I'm not clear on how similar the genocide in Xinjiang is to the process of colonization I'm more familiar with; it clearly has some elements in common, like the Indian Schools, forced relocations, and the mass destruction of religious artifacts and languages, and (in the US) the obligatory United Line of Defense/Pledge of Allegiance. The Stasi-like culture of informers and the hierarchical neighborhood committee structure, however, seems like a significant difference. And the levels of brutality are still, fortunately, comparatively low, compared to those historical atrocities—though still intolerably high in absolute terms.
The historical background is quite different; there have been mosques throughout China since at least the Song and probably the Tang, and many of the greatest Chinese in history have been Muslims (郑和 is perhaps the most famous), and the Uighur settlement of much of what is now Xinjiang dates to the late 18th century, after the Qing committed genocide against the Dzungar Mongols.
This article provides a very useful anatomy of the forms state oppression can take in today's world. Studying it will probably serve anyone well, because these same practices are likely in the future of many peoples, at the hands of many different governments—at least those that prove effective at establishing social control. Tahir Hamut Izgil's present is many, many people's future.
How can we prevent the heavily-stratified societies that generate such profound oppression from overpowering people and territory in this way? Having a culture that doesn't generate that kind of stratification is surely necessary, but it wasn't enough for the Lakota, the San, or the Bayaka.