This feat grants represents your knowledge of the Religion. Characters with this feat are granted special quest-specific dialog options/object interactions that classes without this feat otherwise could not perform. It may also allow certain skill checks to learn insight into specific situations.
Bards and Stormsingers receive this feat at levels 1, 3, 5, 7, 9, 11, 13, 15, 17 and 19.
Verbatim from the release notes: Many classes now gain the "Arcane Lore", "Religious Lore", or "Wilderness Lore" feats every level, which may modify certain dialog options or come up in other ways during quests.
The Lords of Dust: Characters with the Religious Lore feat may purify the altars instead of smashing them. Doing this on all three altars will grant you a bonus chest.
In the Inspired Quarter, the player can talk to an NPC using a certain dialog and gain a reward.
Rest Stop: One of the staves requires Religious Lore in order to disable it safely.
Temperance of Belief: enchantment on Heroic and Legendary Collective Sight, grants Quality MRR depending on the number of Religious Lore feats
Temperance of Spirit: enchantment on Gloryborne Gloves, grants Quality PRR depending on the number of Religious Lore feats
Divine Crusader: the enhancement Mighty Crusade gives AC and PRR based on the number of Religious Lore feats
The Hand and the Eyes: The hunter spirit requires a Religious Lore check (boosted by Wisdom) to speak to correctly (this is part of the optional to make the Marut fight easier or bypass it.)
