Funnily enough, I didn't intend on religion to be such a big topic in this story, but that changed as the story went on...
The main faiths of the 'mon verse are devied up into three brackets.
"Old world religions" aka the more institutionalized faiths like catholicism went through horrible upheaval, inter fighting, and ended up as a mix-match, hodge-podge institute that's taken a little from column a-z that's heavily leaning on the flavor of catholicism but has shadings and mythologies from other institutionalized religions as well.
It's considered incredibly gauche to worship in these places, as most preach either anti-mon philosophy or human-centric viewpoints that are wildly against the common man's norm. But their tales "Genisis" etc are commonly known and bandied about as horror stories or gossip points. Having been osmosed by the common man's culture just for how long they've been about.
Presently these churches only exist only because they are supported by old families, and receive a great deal of fiscal stimulus from their congregations. It's a mark of the rich to be an active churchgoer, and a number of those older hands, traditionalists, in power have ties with these institutes since they support and encourage many of the views of those who favor the past or pro-human attitudes.
It's actually common for low-level or non-combative members of Team Rocket to be part of these congregations and rumored the previous Boss of Team Rocket was a prominent member in her community.
A few chapels of note that exist in Kanto are in Viridian and Violet. Not as grandiose as say... Notre Dame, while sweeping the buildings serve very different purposes. Viridian gets most of its money by being a popular wedding spot, is more sweeping gardens with a building meant to overshadow nature, and uses the various flora to accent the wonders of the building, Violet's is more stark/serious. As a source of power/church government, it glories the sometimes bloody history and wars while being the main source of charity organizations in its region.
Faiths of philosophy: The less formal binding philosophy/faiths are practiced privately in homes, with variations between families. There's little to no centralized force, but rather a small network of roadside shrines that are part road stop, halfway home, used in pokemon journeys, those seeking to reconnect spiritually with nature, calm their minds, or get away from modern society. Locally supported, they occasionally band together in a crisis to assist the people around them, but their no hierarchy and goods and services are the norm of "paying them back" rather than money, so they're generally limited in their fiscal power, by choice.
Legend worship: It's considered dated to worship 'mon as a whole, but in communities situated around Legend hot spots, or places where Legends waged battles, it's common. And it's a common joke to ask someone to swear and what 'mon they swear on tells you what region they're from. There is a smattering of origin stories, creational myths, (some claim Mew is the all-creator, others Arceus, or Gourdon/Kygore) and the like. These are told by town elders/historians, and there are usually appeasement rituals, or rituals asking for the Legends to grant their favored blessings (better strength, luck, clarity of mind) or travel with them, or so on and so forth. As most Legends are merrily sleeping, or apathetic, these rituals don't usually amount to much... but in certain places, like Alola, where a Legend is active, invoking their name/blessing/rituals can have terrifying and immediate results.
A common Alola joke goes:
"Did you hear about the man who swore to Tapu?
"No, what happened."
"Tapu thought he was swearing at him, so the man only did it once, we had to sweep up the trail after."
Presently of the cast of Transversal the main/influencial character's faith goes.
Giovanni: Atheist, raised in Catholic environment
Lillie Aether: Philosophic leanings
Silver: Legend Worship, (this was encouraged by mask, who posed as a Legend of Ice, to scare the bejeebas out of the kids)
Kuki: a more benign example of Legend Worship
Hua: Philosophical leanings
others pending
