BaZi belongs to Chinese Metaphysics (中国玄学), with roots in the Han Dynasty (206 BCE – 220 CE). It was formalized in the Song Dynasty through the classic text Yuan Hai Zi Ping (渊海子平).
It is not a religion. It doesn't worship deities or prescribe moral laws. It rests on Daoist philosophy — the idea that everything is made of qi (energy) flowing through the Five Phases. You can be Christian, Muslim, atheist, or spiritual and still use BaZi. It's a technology of self-understanding, not a belief system.