The Han Chinese are, by far, the majority. Uyghurs are a small and unliked minority. What makes you think they're going to destabilize that nation? Did the poor treatment of black people in the US cause it to collapse? It did lead to a civil war at one point, and to some turbulent times a century later, but that's only because people in the US actually cared about human rights. I don't see any evidence that most of China's population is too concerned with the treatment of Uyghurs, unfortunately.

True for the Uyghurs, but less true for Tibetans. The Tibetan public is largely happy with what has happened under China - it's the deposed nobility who are less excited about it.