"They respect local laws and culture" - I think people from Xinyang probably have a very different perspective on that........
If you had AlQaeda in a hypothetical region near Florida with almost two-yearly terror attacks, you would shit bricks and create jails/prisons with more security than the Pentagon itself.
I think there's a more nuanced version of this: China respects local laws and culture _outside of what they view as China_ more than the US does. It's also worth noting that China's policy in Xinjiang is somewhat narrowly targeted at religion, and less other aspects like cuisine or clothing. That said, religion is nigh impossible to separate from the broader idea of culture in much of the world.
I encountered this almost first person. When American company goes like an elephant, bribing local officials left and right, using dirty practices to push out concurrents. At the same time, Chinese companies try very hard to abide to local regulations and trying to resolve all issues using local courts, etc. Like actually civilised people.
What happens inside China is nothing of my interest, it's their business. They existed for millennias, they probably know how to manage themselves. They are not trying to expand outside of may be Taiwan, they don't put their military bases in my country, they don't fund so-called "opposition" and that's good enough for me.