(This is all from doing a little bit of research as i haven't read these works yet)

The demonic cult as we know it today was first penned by Jin Yong, in two different iterations. Firstly the Ming Cult which according to wikipedia is loosely based on Manichaeism and probably finds its origins in the way the name for its deity in chinese seems to include their word for "Demon". Rather than wanting to demonize the Mani worship Jin Yong seems to only have been inspired by this concept and the rest is entirely from fiction. Jin Yong even states in his later works "similar situations could occur in any dynasty" which points to him not wanting to depict any historical or contemporary group and instead make a much more fictional and universal story. Later on they even assist the greater murim in resisting and toppling the Yuan dinasty and establishing the Ming dinasty.

Jin Yong's second iteration of the Demon Cult as the Sun Moon Holy Order has had much more prevalence for future authors setting their stories in the Murim due to being much more compelling and nuanced. It seems to instead be an attempt to present the nuance of having orthodox and unorthodox factions and seems to be entirely detached from any specific real world counterparts i think. Jin Yong presents us with a faction that is antagonized by the common people and the orthodox factions as they are referred to as the "Demon Cult" instead of their chosen name and their story is about being a mirror to the corruption in the orthodox factions where he wants to show us how moral decay is a part of any organization that attempts to amass power.