Well while China can do it. I wouldn't recommend it.
China so far maintained it's non-military intervention policy, which it shouldn't sacrifice at any cost. Going forward this is going to be one of china's biggest tool to grow more influential because every nation around here despise other's boot in their coutry. While Kashmir needs to be separated, It shouldn't come at cost of China's long term image.
My suggestion would be, China should strengthen Pakistan to do it rather than them doing it. West/EU isn't going to be "sympathetic" to oppressed people. They are only sympathetic to their own interest. Rest of the world will either be neutral or supporting China-Pak morally. But for long term, it is absolute imperative that China doesn't use their growing military capability in any third party intervention. World will be watching this closely which is going to the cornerstone for other countries, specially smaller counties, to decide how they are going to view their relationship with China.
I agree that China shouldn't deliberately start a war with India
Plus you have to be realistic about China's non-military intervention policy.
When Vietnam thought it could have a military alliance with the USSR in the 1970s/1980s, the Chinese military were very aggressive in reminding Vietnam that they were just a pawn to be used by the USSR.
At the time, the US was more than happy at what was happening to Vietnam, and its "ally" the USSR.
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Yes, if China is seen as imposing/forcing Kashmiri independence with its military, then it would be bad for China's image.
But if the Kashmiri people decide to rise up against their Indian Army occupiers, China would be sympathetic.
Particularly if China-India were already in a war, and China provided a moderate level of support, like blocking the few narrow mountain roads that lead into Srinagar.
Ultimately, 9 million Kashmiri Muslims can completely overwhelm the Indian Army occupation forces in Kashmir if isolated from reinforcement by the Indian Army, and everyone knows this.
We've seen what mass protests can look like with Hong Kong or Black Lives Matter. And those were largely peaceful protests, from people working in the existing system. But with the BJP revoking Article 370 which guaranteed Kashmir's autonomy, there is no existing system to work with. BBC article below
Also remember that the Indian government stripped the Kashmir police of their weapons before the revoking Article 370, because they feared a rebellion by the police. Voice of America article below on the Kashmir police.
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At a grassroots level, everyone would acknowledge that the Kashmiri people would be better off without their Indian overlords.
It would also demonstrate that there can be *hard costs* to going against Chinese interests.
At the moment, Kashmir is an impoverished police state where nothing works and is cut off from the world.
In the aftermath, Kashmir would be open to development, and presumably become part of CPEC.
That would connect Kashmir to China, Pakistan and the rest of the world.
It would also demonstrate the clear *benefits* of aligning with China.