I would think it doesn't matter what you call the religion just the type, so you could have state religion which would imply graeter control over the popualtion but would have adverse effects on other factors such as science, or if you had freedom of religion it could affect a countries attitudes to other countries with a state religion.
Now that I have typed this for that point you would need to have the religions named for them to affect relations with other countries.
Now that I have typed this for that point you would need to have the religions named for them to affect relations with other countries.
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