Buddhism first entered China from India at about the time of Christ. Over the following twenty centuries, and in many forms and “schools”, Buddhism dominated religious life and belief in China. It adapted and absorbed many aspects of Chinese indigenous Taoism and Confucianism as well as some aspects of Animism.
The emperor as the “Son of Heaven”, and the mediator between the gods and man, gave a nationwide legitimacy to Buddhist beliefs and practices. It also exposed the emperor to being deposed by revolution when the harvest failed and the nation judged he had lost the “Mandate of Heaven”! Roman Catholic mission efforts were trivial in scale when compared to the thousands of monks and scholars out of India building shrines and temples throughout the country. The Catholics also suffered the disadvantage of having no “Son of Heaven” or equivalent role for the emperor and expecting the emperor to recognize the primacy of the Pope on religious belief and practice was an insurmountable handicap to acceptance in the Imperial court.
Buddhists were not overtly hostile to Protestant missionaries who first arrived in China beginning about in 1850. The people of China, similarly, felt at ease considering another new religion because they were at ease with their own overlapping beliefs and practices ranging from ancestor worship, multiple “special purpose” deities represented by idols in the local temple, “feng-shui” spirit concerns etc.
My father often accepted the hospitality of Buddhist temples both for overnight accommodations, and a place to assemble those in the to hear Christian invitations to attend local meetings, and perhaps enroll in “Christian Inquirers” classes presented in the community. Both Christians and Moslems had a religious concept at the time foreign to the Chinese approach to religion -- they expected exclusivity as expressed in second part of the first commandment -- “Thou shalt have no other Gods (before me).