Wanting to form an Islamic state in the middle of a non-Islamic country is not a legitimate complaint.
That's not the Uighur goal. All they're looking for, realistically, is the right to run their own internal affairs and to freely practice their religion without government oppression (this second goal is shared by Chinese Christians, too).
The policy of the Chinese government is to move Han Chinese colonists into the area until the Uighurs are a minority in their own home. Part of this policy involves actively seeking to stamp out the Uighur language, religion and culture.
In such a situation, I can't blame the Uighurs for resorting to violence. I'd probably be blowing up police stations, too.
It isn’t in the middle of China, it is on the northwestern chinese border in a primarily muslim turkic region and has always been such. All people have the right to sovereignty and self determination. While it shouldn’t be our business to get involved. We shouldn’t be deriding a group of people for trying to break away from the Chinese communist hive. From what I can tell, the majority are nationalists and want to be left alone, they have no bad intent to the western world. As long as they stay in that region and don’t come to the west or attack us I have no problem with them