The phrase three teachings, used across the region for Confucianism, Buddhism and Daoism, describes an arrangement that western categories handle badly.
For long stretches of East Asian history a person could participate in all three without contradiction, because they were understood to do different work: Confucian ritual for family and public obligation, Buddhist rites for death and the afterlife, Daoist or local practice for healing, exorcism and calendar. Households sponsored funerals in one idiom and weddings in another. That is why census questions asking for a single religious affiliation have always produced strange results in this region, and why the atlas records participation alongside identification.
Combination went further than coexistence in places. In Japan, kami and buddhas were systematically identified with one another from the ninth century under the honji suijaku framework, in which local deities were understood as manifestations of buddhas; shrines and temples shared precincts and personnel for a thousand years, until the Meiji government forcibly separated them in 1868.
There was also genuine conflict. Chinese states suppressed Buddhism several times, most severely in 845, on grounds that included the removal of land and labour from the tax rolls. Confucian scholars attacked Buddhist doctrine as foreign and antisocial. The picture is neither seamless harmony nor sectarian competition, and the atlas records both the combination and the persecutions rather than choosing an emphasis.