Different gods are more popular in different parts of the 5 Kingdoms, but in political terms, the temples are mostly uninvolved. There is one organization however, which serves as an overseeing administrator of sorts, spanning all the gods, and known as The Temples.
Oftentimes, a single temple will house altars for several gods, even if there is only a single priest. This is possible, because The Temples teach their Keepers the ways of all the gods, at least in terms of basic rites and rituals. Each Keeper usually worships one god personally, but will assist where possible in any matters related to the religion represented in their temple.
The Temples is not a military organization and have no army. They do not engage in conflict between nobles. They claim to be exclusively focused on internal matters between followers of the various gods.
Conspiracy theories claim that The Temples have a secret society within itself, and though its exact purpose is anyone’s guess, the rumors range from secret assassins to hidden advisors to the kings, and everything in-between.
There has been some tension in the past, between the Arcanum and The Temples, as the use of Divine magic cannot be regulated by the wizards. However, nothing more than sharp words has come of it yet.