Religion can be a powerful force, including in anime and manga. Having faith in a higher power, or just faith in general, can move mountains, tame seas, and aid humanity into a brighter world.
The opposite, however, is also true. Some take their faith to extremes, and consequently cults spring up. A lot of anime and manga deal with cults or cultish behavior masquarading as religion, whereas others play religion entirely straight. Some even derive power from their religion, dating back to myths of the clergy, among other things.
Disclaimer: All of these examples contain spoilers as to the nature of these religions and their story significance.
While these ten anime and manga have their own religion, they do follow some rules -
Rule 1: These religions must be fictional. Any resemblance to real world religions is automatically discarded, or if it pushes too much into the real world.
Rule 2: Simply having gods does not a religion make, it must have an organization or recognition of faith of some sort to count.
From Attack on Titans Church of the Walls to the many religions in One Piece - 10 ficitional anime and manga religions
1) The Church of the Walls - Attack on Titan
There is a church dedicated to worshiping the Walls keeping Paradis safe from the Titans. This religion ultimately believes the Walls to be sacred, and should be kept free and clear of "impurity," such as rails, humans, and even wall mounted artillery used to keep people safe. The truth is far more horrifying and the church is in on it.
As seen many times, but particularly throughout Attack on Titan's Royal Government Arc, the church is allied with the notorious Reiss family. Essentially, many high-ranking members of the church are devoted to keeping the Wall Titans a secret to the point where Pastor Nick is tortured and murdered after aiding the Scouts.
By the time of Historia's reign, the church was all but defunct. Many of their members were either eaten, killed, or arrested.
2) Adai's Gunmen worshiping village - Tengen Toppa Gurren Lagann
The isolated underground village of Adai in Gurren Lagann is where Rossiu Adai originates from. It is also a village of about 50 people, which cannot exceed 50. It also worships Gunmen, a large mecha in Gurren Lagann. The village also views the surface as a celestial land. Two people are randomly selected to be "sent to heaven" as a sacrifice.
This illusion is upheld even when a hostile Gunmen stumbles underground and tries to attack the village. The Gunmen is repelled by both the "God" Gunmen and Gurren-Lagann, with the head priest piloting the Gunmen. While two orphans (Gimmy and Darry) are forced to go to the surface, Rossiu joins them and team Dai-Gurren.
The village is revisited later in the series when everyone is on the surface and is emptied. Rossiu attempts to take his own life, but Simon is able to stop him. It's unknown if the religion persists, though implied it dissolved after the 7 year time skip.
3) The LOL Cult - Mob Psycho 100
The LOL cult in Mob Psycho 100 was a creepy false religion spawned by an evil spirit called Dimple. The religion gathered many members over the course of a month. The followers were used by the spirit to try to become a god, and wore masks that induced uncontrollable laughter.
Dimple had a hex on those masks, and was able to control people with them. It was rather unsettling as many people were forced to laugh, reminiscent of The Joker's lethal laughing toxin. When Mob defeated him, the hex that was on all the masks inducing uncontrollable laughter lifted. It freed all the members of the cult.
Unfortuantely, some of the former cultists then formed a new cult around the Divine Tree and a being known as Psycho Helmet. While Psycho Helmet may have been under Dimple's control, it retained its mass hypnosis abilities and desire for world domination.
4) Jashin - Naruto
While the Otsutsuki might as well be God in the ninja world of Naruto, the fact is that there wasn't quite a large religious gathering for them as Jashin was. Jashin was a god worshiped in Jashinism, known to Hidan and several others like Ryūki. This religion is mostly known for demanding major sacrifices and promoting death and destruction.
Naturally, it's a perfect fit for a sadist like Hidan. Especially when one considers how he had zero moral restraints against who he killed. An official investigation uncovered a sect of Jashinists who kidnapped travelers to sacrifice. It's a bloody relgion that ultimately was dissolved thanks to Hidan's death.
On a side note, Jashin's followers were able to use voodoo links that could link targets provided they ingested their blood and were within range of Jashin's symbol. It sounds like a religion that Himiko Toga of My Hero Academia would join.
5) Humarise - My Hero Academia
Speaking of cults, the Humarise organization from My Hero Academia is a rather curious case. Their creed is based off the belief in the Quirk Singularity Theory, a rather baseless conjecture stating that Quirks will become increeasingly powerful to uncontrollable levels.
Of course, the members of the cult hate and despise Quirks for this reason, even calling them diseases. It's eugenics by any other name, formed into a religion. They even took matters further by detonating a Trigger Bomb in a city, killing off Quirk using people and leaving only the Quirkless alive.
While the theory itself continues to brew around, Humarise itself was stopped thanks to a global effort. It's a good thing too, as they had Trigger Bombs placed worldwide.
6) Zentopia Church - Fairy Tail
The main religious body in the Kingdom of Fiore in Fairy Tail is arguably the first beneficial religion on this list. Whilst they are independent from Fiore, they do serve the state and try to aid people. Of course, their history is complex. Long story short, the Zentopia Church was founded by people who survived the chaos caused by The Infinity Clock.
They dismantled and scattered the pieces of the clock, and one of their own even created a biological link spell between disciples to seal away an Amplitude Limiter to prevent Real Nightmare from being unleashed again. They were all under mind control to rebuild the Clock until the Fairy Tail Guild helped them out.
The Church seeks to aid people, and is genuinely a good organization.
7) Ishvala's religion - Fullmetal Alchemist Brotherhood
While many Ishvalans were massacred and the land itself destroyed, the culture and faith lives on in the survivors. The religion has been interpreted as forbidding alchemy, calling the practice "perverse and arrogant" because of the implications that God created objects could improve with human hands.
Whilst this may put it at odds with alchemy in general, Ishvalans were a peaceful people before the schemes of Homunculi and Amestrian Central Command had them raze the city to the ground. All that to replicate what happened at Xerxes on a massive scale.
Ishval is revitalized as of Brotherhood as a Holy Land and the new government aids in regrowing crops and rebuilding homes.
8) The Vodarac - Eureka Seven
Another peaceful group that found itself under attack was the Vodarac in Eureka Seven. They are a group of monks that believed true peace lies in with connecting with the land. They believed that the land was sentient due to the intelligent lifeforms known as the Scub Coral landing 10,000 years ago.
They were frequently discriminated against and nearly eradicated by Antibody Coralians and the United Federation Military. Fortunately, they survived as into two groups. Unfortunately, one faction turned heavily violent and ultimately sacrificed themselves.
In the end, the Vodarac undeer Norb are able to merge with the Scub Coral and depart from the planet in relative peace.
9) The Holy Sol Temple - Fire Force
The Holy Sol temple is the dominant faith of the Tokyo Empire in Fire Force. They are tied closely with Sovereign Raffles III. The church is ultimately exceptionally shady, though religious characters like Iris exist to counteract this. In other words, faith is seen neutrally in the series.
The church is revealed to be in league with the Evil Evangelist and White-Clad. It follows on the theme of organized religion being corrupt and evil and wanting to start an apocalypse. They even have assassins that ultimately try to kill anyone who would dare to oppose them. It's why Company 8 exists in the series, to serve as Internal Affairs.
The church was eventually stopped, but it takes a lot to do so. Given how well connected they are and the amount of forces at their disposal, and that it surprises the protagonists.
10) Many islands, many religions - One Piece
While this entry could be used for the Celestial Dragons, or Nika, the fact is that One Piece's world is vast and has many paths of faith. Some are active, like the Skypedia "Gods" or the Satanic cult in Namakura Island. Others, like the Kashigami worshippers of Shandia, have ceased due to having been under the influence of Tree Fever and when the massive serpent was killed.
The biggest, or at least the most important religions, seemed to be the World Nobles/Celestial Dragons, the Sun God Nika, and several curses and kings from the Fish-Man races. While the World Nobles are nothing more than men, the Empty Throne and Im might be a god considering the weapon used to destroy the Lulusia Kingdom wiped out the country.
It's worth noting that the Nika religion spawned the myth that Gear V Luffy seems to embody, but time will tell if that's true or not. As stated prior, One Piece is vast and diverse in not only characters but religions.