What makes you think that the world cares so much about Uighur culture? Myanmar rohingya crisis is a clear proof that the world is not very keen to fight for human rights even when the cost is low (compared with a China conflict). And this is the hard truth: If the rohingya were to be displaced in big numbers in the US or any of the developed countries(maybe with a few exceptions) I'm pretty sure they would be turned back/stopped at the border.