> Non-Muslim Uyghurs who make themselves useful for the government don't seem to be doing so bad for themselves

The fact that certain individual Uyghurs are not targeted is not evidence that the reason oppressed Uyghurs are being oppressed is not "because they're Uyghurs". It's evidence that being a Uyghur can be mitigated.

But if you prefer, "because they are members of a group with very questionable allegiance". This phrasing picks up the other Turkic groups in the area while still clearly excluding the Hui.