> the depression of the muslim Uyghur by China
This is not a religious conflict. China has oppressed the Uighurs because the Xinjiang region was only brought under full Chinese control late, and the Uighurs have been relatively independent-minded.
That this conflict isn't about Islam per se is evident from the fact that 1) there is a substantial Muslim population within China outside of Xinjiang, and those Muslims have not been given the same brutal treatment, and 2) there have also been secularist voices of resistance among the Uighurs to Chinese control of Xinjiang.