I'd argue that Buddhism is a religion with multiple philosophical schools contained within its traditions. Buddhism is a religious system due to its emphasis on spiritual practice and the importance of the spiritual community (Sangha) to all major Buddhist sects; it is an organized religion. Of coarse, philosophy underlies all Buddhism because at least one "philosophy" (as in a way of interpreting the world) must be present in a religion. However, Buddhism contains a rich history of diverse philosophical "schools," such as Middle Way, Mind-Only, and so on that developed from various interpretations of the core (and later) scriptures. Traditional Buddhist scholasticism and philosophical debates did much to allow the formation of the various schools, which I don't think was a bad thing. Of coarse, some sects (notably Nichiren Buddhism) started largely from the views and activism of a sole charismatic monk, though this doesn't seem to be true of most surviving sects.

Confucianism seems to be in a similar category, albeit leaning more to the philosophical side than the religious side. Nevertheless, devoted practitioners do see it as an organized religion that promotes ancestor worship as well as the honoring (if not deification) of Confucius.

Taoism seems to be either a philosophy or an organized religion depending on the context. The "yin and yang" and "universal harmony" ideas have been widely adopted by Confucians and Buddhists in China and beyond. However, it is also an organized religion attached to temples and (at least prior to the Maoist Cultural Revolution) monasteries. From what I can gather, Taoism as an organized religion is most similar to the Shintoism of Japan but also shows influences from both Buddhism and Confucianism; that is, it takes much from the "historical Chinese psyche."