One also wonders who the leftists are in Xinjiang. They can't possibly be the locals.
Han make up more than 40% of the population of Xinjiang and there has been a significant Han presence in the province since it was conquered by the Qing in the 18th century. Uyghurs make up less than 50% of the population, and it's not as if all or even most of them are Islamists or nationalists.
Also, re: Inner Mongolia, it has by some accounts the fastest growing economy in China and has lots of natural resources. The population has grown significantly as many people from the Beijing area and elsewhere move to the province. There is also a lot of wealth disparity, as you guessed, between the Han majority (about 80% of the population) and the Mongol minority (around 17% of the population) though the Mongols are much better integrated than the Uyghurs are. One mindscrew statistic is that, despite making up such a minority, there are actually twice as many Mongols in Inner Mongolia as there are in Outer Mongolia!