It is clearly about religion. Read the UN report or the first sentence of the linked article:
“China has secretly built scores of massive new prison and internment camps in the past three years, dramatically escalating its campaign against Muslim minorities”
On a separate issue, the CCP is also rounding up trouble makers, and people that refuse to follow along and learn Mandarin would definitely qualify.
The "Muslim minorities" line is a trope used in Western media for the last couple of decades, especially in the wake of more interest in the Muslim world following 1990s and early 21st-century Islamist terrorism, but it obscures the fact that many Uighurs are non-religious or outright anti-religious. China is pleased at this "Muslim minority" angle that the Western media and NGOs use, because it can spin oppression of the Uighurs as a crackdown on Islamism. However, as I said, religion per se is not the issue here. The problem for Beijing is that Xinjiang has been too independent-minded, because the Uighurs (unlike most of China's minorities) only came under Han domination recently.
Kazakh, Kyrgyz and Hui Muslims in Xinjiang are subject to the same policies; the thing they have in common with Uyghur Muslims is that they're, well, Muslim, and that Kazakh and Kyrgyz speak Turkic languages.
Meanwhile, the Chairman of Xinjiang is Shohrat Zakir, an Uyghur politician and (of course) Communist Party member. Being non-religious or anti-religious is a good way for Uyghurs to make career in service of the Chinese state.
I also doubt that Uyghurs are somehow more independent from Chinese rule than other people in China, especially with respect to history, considering the supporting role of Uyghur troops in the genocide of Dzungars (who used to live in modern Xinjiang) by the Chinese Qing army.
What Kazakh, Kyrgyz and Hui Muslims have in common with the Uighur here is that they are fellow minorities from Xinjiang who were also subjected to Han domination only recently. Moreover, the Kazakh population is often seen as a fifth column due to a titular republic for their own people being located right next door.
Citing Shohrat Zakir is disingenuous. In the Soviet Union it was common for people to point to members of the ethnic minorities placed in official roles and say "See, there is no discrimination or oppression”, and the exact same phenomenon holds for contemporary China though it is much less talked about. But those ethnic-minority bureaucrats or politicians invariably made compromises: they did not particularly insist on using their own language in officialdom or defending the rights of their ethnic kin to do the same, and when they did publicly use their native language it was merely in the service of propaganda initiatives directed by the central government. But those Communist Party members who have insisted on the dignity of China’s minority languages and called for resisting Han assimilation have, as I said, suffered persecution for it.
The Uighur definitely have been independent-minded. Regardless of military collaboration with the Qing, the average Uighur would not have had so much exposure to Han culture and language until recent decades.
“China has secretly built scores of massive new prison and internment camps in the past three years, dramatically escalating its campaign against Muslim minorities”
On a separate issue, the CCP is also rounding up trouble makers, and people that refuse to follow along and learn Mandarin would definitely qualify.