In the early 18th Century, the Jesuits and the Dominicans took differing views on their missionary work in China. The Jesuits took the position that since the traditional chinese folk religion practices were civil in nature and thus were permissible for catholic chinese while the Dominicans took the view that they were religious in nature and thus incompatible with christianity.
Pope Clement decided in favour of the Dominicans upon which the Emperor Kangxi, who had previously been inclined to allow the Jesuits to perform their missionary work, banned Christian missions in China.
If Clement decides in favour of the Jesuits, could we see an integration of Confucianism and Catholicism? What might the effects on China be?
The situation in China would probably would not be that much different than any other place colonized by "Catholic" nations. Aspects of indigenous religious beliefs exist among the Native American peoples of South America, for example, and Voodoo is a syncretic mix of West African religion and aspects of Catholicism. If Pope Clement rules in favor of the Jesuits, then I would not immediately see an immediate social conflict between people hearing Mass publicly and then engaging in ancestor worship privately. It is very hard, in my estimation, to prohibit indigenous practices. Perhaps the Jesuits recognized that, and were willing to overlook some indigenous practices in order to further catechise the Chinese and possibly indoctrinate them in steps.
The conscious blending of Catholic and traditional Chinese practices would be a major problem, however. This might have been accelerated by the substitution of classical Chinese for Latin at the sacraments. The Roman Mass has been said in other languages before -- Church Slavonic was used in Croatia and I believe among the Czechs, possibly others. However, these countries were thoroughly catechized through the use of Slavicized rites. I don't think that that would be an analogous situation, given that the texts of the sacraments remained the same in Slavonic and Latin. But to translate the Mass into classical Chinese without a longer period of catechesis might cause a blending of traditional Chinese practices into the framework of the Mass and other sacraments. Perhaps Pope Clement was afraid of this, and sided with the Dominicans in order to protect the integrity of the sacraments.
I think it would be fascinating to see Mass celebrated not in European-style vestments but in the court vestment of medieval China. Or medieval Japanese court vestments, if the Jesuits were able to stay in Japan longer, get established, and translate the Mass into literary Japanese. Of course, modern Chinese Catholic and Japanese Catholic priests wear chausables and dalmatics per the rubrics.