The major events events of the Cultural Revolution (1966-1976) were largely associated with "China proper." The historical border regions acquired by the Qing Empire that came under Chinese control after the Xinhai Revolution of 1911 were not major focal points for the movement as a whole. However, that does not mean that border regions (Xinjiang, Yunnan, Inner Mongolia, Tibet, etc) were not affected.

Of particular note was the parallel persecution of religion in both Han and non-Han contexts. Confucius and other ancient Chinese philosophical/religious traditions were routinely attacked by Communist Red Guards seeking to purge "superstition" from the new, modern, socialist society. This included the raising of an unknown number of temples and shrines across the PRC. The legacy of this is still very obvious today. If you have ever been to Taiwan, especially Southern Taiwan, it seems that every street has a small shrine or a temple. Most of these are privately-owned and the size of a single-car garage. Chinese cities, conversely, have virtually no temples, outside of officially sanctioned museums and historical sites. Rural areas fared much better, with many of the small family, ancestor-worship shrines surviving the Cultural Revolution. The most dramatic parts of this iconoclastic fervor was the Four Olds Campaign, which began in 1966. "Four Olds" or 四旧 referred to Old Customs, Old Culture, Old Habits, and Old Ideas. The Criticize Lin, Criticize Confucius campaign (1973-1976) was another major iconoclastic campaign. I'm not going to delve too much into this, however. The main takeaway from this should be that religion was a prime target during the Cultural Revolution.

For Muslims in Xinjiang, Gangsu, Ningxia etc., this meant that many mosques were torn down. There are some accounts of Qurans in Xinjiang being burned, although these claims have been difficult to verify. This is not because it would be out of character for Red Guards or PLA elements, but rather such efforts were so widespread and poorly documented. The kind of public criticisms (when an individual would stand before and community and admit "failures" and receive punishment") were also a feature of the Cultural Revolution in Xinjiang and elsewhere. Imams and other religious figures were subject to particular ire, with some being paraded in the streets and humiliated. The most tragic event, however, was the Shadian Massacre in Yunnan. Shadian was a small town of mostly Hui (ethnic Chinese Muslims). The PLA had shut down mosques and burned religious texts. Some 1,000 residents the town attempted to lobby the government in Beijing to reinstate their constitutional rights by traveling to the capital. Some residents took control of barracks and acquired/manufactured weapons, resulting in a massacre of some 1,000 Muslims in 1975.

If it sounds like this is vague and general, that's because it is. The Cultural Revolution is one of the least documented major mass-movements of the 20th century, and archival access to documents from that era has declined rapidly under Xi Jinping. Exact numbers for those killed and for iconoclastic incidents are impossible to obtain. I also realize that much of this is not directly related to Xinjiang, unfortunately archives in Xinjiang are especially difficult to utilize. I'm sorry that I couldn't give you more information. However, I think it gives you a good idea of the experience of Muslims in general under the Cultural Revolution. It was during the 1980s and 1990s when mosques began to be rebuilt across Xinijiang, Gansu, and Ningxia. Today, many of them are being torn down once again. The parallels between what is happening today and what was happening in the 1960s and 1970s are stark to say the least.