Tibet, China, Korea, Japan, Mongolia, Southeast Asia, and notably Bali have all managed to resist becoming majority Christian or Muslim countries. Though it should be noted that this is only a strict reading of your question regarding these countries' indigenous religions. Most of them were replaced by other traditions: Buddhism for the most part. Korea, which is very complicated religiously today (with a majority of the population being non-religious, and roughly a quarter Christian and a quarter Buddhist) certain has a very loud and powerful Christian population. Japan is in a similar boat, though the Christian popualtion is lower, with the Buddhists and Shinto still existing in high positions of power. China has a huge Christian population, though China's strict laws concerning religion make it relatively difficult to get numbers regarding religious demographics in the country. It's also worth mentioning that these countries in East Asia are highly syncretic: with Buddhism, Taoism, Confucianism, and indigenous religions existing side-by-side and often in the same temple and monastery. In Southeast Asia, Tibet, and Bhutan, Buddhism is very much the majority religion, and even though they have made Buddhism very much their own (similar to how East Asia has its own flavors of Buddhism) it is still technically a foreign religion (from India) and missionaries from the West or the Middle East have had historically notorious bad luck in gaining converts, minus pockets of Islam like the Rohingya people, and of course subtracting Indonesia, the largest Islamic nation in the world. Bali is a notable exception (to the exception of Indonesia, no less) which has managed to maintain its unique Hindu faith and culture throughout the centuries.