I've been to Xinjiang also (Urumuqi and other parts of Beijiang). I didn't see a Uyghur get beat up or anything, but this was (a) way back in 2006 before the riots of 2009 and (b) I don't think we would notice much as tourists even IF there was something going on.
Beijing used to have a lot of Uyghurs before the 2008 Olympics, but they were mostly all driven out and not allowed to return after the event.