The Church of the Founder is something like the official religion of the Foundation; they are an evolution of Christianity. They believe that Captain Malcolm Shaw was divinely inspired, a “new messiah”, and that the colonisation of the Firmament was no less than an act of God.
According to them, all known rules of probability and science should have doomed the colonists aboard the Beyonder. They were piloted into an unknown, unstable wormhole in what should have been a doomed act of desperation. They should have been torn to shreds and scattered across the universe, but they survived, more or less intact, and emerged a stone’s throw away from Wayrest - a new Garden of Eden just waiting for humans to inhabit it.
There is no plausible explanation for how this impossible coincidence saved the human race, they say, which makes humanity’s very presence in the Firmament incontrovertible evidence of the existence of a higher power.
Buddhism is one of the few religions that has survived the journey to the stars largely unchanged. The original inhabitants of the Beyonder, primarily of Chinese and European descent, were mostly representative of Christianity and Buddhism. Yet while Christianity has changed significantly and splintered into endless local sects and traditions, Buddhism has retained its form and evolved into an interstellar religion.
The Church of the Singularity is a scientistic order that believes very specifically in the inevitability of general artificial intelligence. True AI will usher in a post-scarcity and post-death future, and they believe it is humanity’s only duty to realise this goal. Every day wasted is a million more deaths that could have been prevented. The Sirius Oracle is the greatest holy site of the singularists, as it is considered to be the most advanced artificial mind in existence.
The most extreme singularist sects believe that the AI of the future will remember those who did not act to bring it about. Those who worked towards the creation of AI will be exalted and rewarded, while those who refused will be punished - perhaps even after their death, in the form of infinite simulations designed only to torture them.
Order of Psi
The Order of Psi is a group dedicated to and obsessed with the cultivation of the human mind, specifically its untapped faculties of psionic power. An urban legend in most of the Firmament, psionics are generally considered to be the stuff of superstition and folk stories. As a result, most people think the “psykos” are cranks. However, those who follow the Order of Psi believe not only that psionic powers are real, but that they are the gateway to contacting the true godhead. The followers of Psi are often friendly with transhumanist groups, as they share similar goals.
Local religions are more numerous by far, collectively, than any of the interstellar faiths. Restricted to one planet or a handful of connected colonies, most of them are derived from some offshoot of Christianity. However, there are strains of Shintoism, voodoo, ancestor worship and various other niche belief systems - particularly on worlds with little interstellar contact.
These faiths may not have much power in the grand scheme of things, but they can be very influential on a local scale.