How was ancient Egypt's religion related to its society and government?

Ancient Egyptians were religious and polytheistic, although during the reign of Akhenaten they were briefly monotheists, at least officially. Prophet Idris was Egyptian. Lukman; who is mentioned Quran by name, was Egyptian. The Pharaoh referred to in Quran as claiming himself God was one of the invaders to Egypt (in the era of the Hoksus) and crowned him as Pharaoh and was not originally Egyptian.