Cult of Hope
Ever since 2011, Homura had payed her respects to a "goddess" whom she implied was once a friend of the Mitakihara Four. The others in the group humored her, but never took it seriously until the Battle of Epsilon Eridani, where Homura proved impossible to kill, whether by soul gem expiration or otherwise. Kyouko, witnessing this, along with what might be the only recorded use of black magic in the new world, reconsidered whether Homura's delusions might actually be truth.
On the first anniversary of the battle, Kyouko gave a speech, sharing Homura's beliefs (as she understood/interpreted them) with the world, and launching the Church of Hope. Since then, it's expanded rapidly, and holds the singular honor of being the only religion, in an age of silently-Governance-encouraged secularism, to be consistently gaining membership.
The Cult of Hope is superficially a Christian offshoot, but fundamentally differs from mainstream Christian doctrine in several respects. Most critically, it considers God to be benevolent but unable to understand humanity, holding humans to unworkable standards, which could only be reconciled with human nature by the intercession of a mediator/savior. In the case of "normal" humans, this was Jesus. In the case of magical girls - whose doom was not a spiritual hell, but a physical one (the nature of which Homura had never revealed) - it was the Goddess, who comes to claim magical girls whose soul gems turn black. Thus, the Cult worships Madoka, despite her technical humanity, because they consider her to be more relatable and worthy of veneration than a distant and out-of-touch Creator.
The Cult of Hope are the current custodians of the Ribbon, a relic of the Goddess provided by Homura before she vanished. It has been known to occasionally give people visions, which are somehow "cosmically censored" from any technological or magical transcription attempts by third parties.
So far all the known visions have been to magical girls. As the Cult of Hope doesn't give anyone else access to the relic, whether this is a fundamental limitation of the artifact or merely selection bias is unknown.
The Cult is headquartered in Mitakihara, at a rebuilt version of the church which used to be presided over by Kyouko's father.