Thinking of people like Matteo Ricci. In Europe in the 16-17th century there were conflicts with Muslim empires etc and images of Muslims as a threat to Christianity. And of course they were expelled or converted in Spain. When Jesuits went to China did they feel they had more in common/a kind of kinship with the Muslim population, was there any extensive contact, any attempt to convert the Muslim population, and did the views of Muslims held in Europe influence how they were viewed? And vice versa, how did the Muslim communities react to any Christian missionaries they found? Did interacting with the Muslim population of India and Muslim communities in China, SE Asia etc change how Islam and Muslims were viewed in Europe? Did the missionaries (and Europeans at home) differentiate between Muslim communities at all (did they define them purely by religion or were different ethnic groups viewed differently)??
I don’t know if the Jesuit missionaries visited the regions with large Muslim populations such as xinjiang but a book I was reading has mentioned Muslims in China a few times, discussing some who were members of the civil service. So presumably they were encountered in daily life across areas with missionary work.
Focusing on Matteo Ricci, he was in China from 1581-1610, during the Ming Dynasty. At that time Xinjiang (New Province) was not part of China. The Uighur Muslims of Xinjiang are quite different from the other Chinese Muslim population, the Hui, a group of converts who are ethnically and culturally far closer to the Han. They are located throughout China but concentrated on the coast, especially the South-East where foreign Muslim merchants were most active.
Ricci and his colleagues were aware of them, although it's unlikely he met any personally. Writing in a letter he said "someone has told me that the many of the Moorish faith, who live in this country, buy this book, for it seems to them that it speaks of God better than the books of China". The fact he refers to them as Moors (and alternatively Saracens) speaks to his opinion of them. In his mind, and the Jesuits in general, they applied an identity on the Hui borne out of their own background in the Mediterranean. They viewed them not as authentically Chinese, or a different kind of Muslim, but an extension of the middle easterners they were familiar with. In his writings Ricci paints Islam as alien to China. He did this for Buddhism aswell, it was part of an effort to present Catholicism as more compatabile with Chinese culture than any of these "rival faiths". Indeed Ricci did view the Hui as rivals, but expressed surprise that they were not actively trying to spread their faith as he was. As his writings on the Hui varied little from European preconceptions, they did not have a significant impact on European opinion.
Edit: Ricci did indeed express a sort of kinship with Chinese Muslims, as is expressed in his letter commenting on the popularity of his book amongst them. This was not shared by the Hui however. They viewed the Jesuits as representatives of a Western faith, not a fellow abrahmic one.
The effect of Jesuit missionaries on the Chinese Muslim community was profound. It stimulated in them a reaction common to all of Chinese society coming into contact with the Western knowledge the Jesuit disseminated. Liu Zhi, for example, borrowed ideas from Ricci in his work Tianfang Xingli (Nature and Principle of Islam), the largest Hui work on cosmology and nature.