In my experience a lot of the population is very anti-Uighur and they wouldn't care that much. In the run up to this people have been conditioned by images of violent protests in the region. They have been demonized as religious fanatics. Religion in of itself is a big no-no in China. You combine that with anti-Muslim sentiment and a different ethnicity and it's pretty easy to demonize a group.

To convince them you'd really have to go into details and explain just how unjust the whole ordeal is. Most pro-govt people's default assumption will be they're doing a good job taking care of bad people.

Even the notion that someone of a different religion and ethnicity who might not speak the language should be rightfully considered a Chinese citizen deserving all the same freedoms is a tough sell.