Actually the five elements and eight Trigrams is the core of Chinese culture.
All the Chinese school of thought, from Taoism to Confucianism to TCM to Art of War, all originated from the book of changes.
I actually think that the Chinese have separated a lot between religion and philosophy - or the religious and the philosophical aspects of traditional beliefs. Philosophy was what the intellectual elites accentuated, religion and simple faith was a folk thing and more often than not it was frowned upon by the scholars. (Xunzi or even Confucius come to mind.)