The Religion thing means they can do stuff specific to that religion, and/or they become manes/angels when they die.
Some spells are tied to the religion of the unit. Like mask (become hidden nationality). Only Heroes and High Priests (I think) abandons you for a religion change. And Royal Guards abandon you if you switch from Aristocracy.
Some spells are tied to the religion of the unit. Like mask (become hidden nationality). Only Heroes and High Priests (I think) abandons you for a religion change. And Royal Guards abandon you if you switch from Aristocracy.