What would be wrong with having a missionary Rogue? Religion has nothing to do with role.
Remember, Wizard, Cleric, and Pally have religion. Not just Divine guys.
Sure, there's nothing wrong with it.
The problem is that a character gets more out of it if he hasn't a class fitting the background:
If you have a class like the cleric, you get a language and a skill bonus.
If you have a class like the rogue, you get a language, an extra class skill and a skill bonus.
As a non-religious class, you get it on your class list, meaning you can pick up the skill without burning a feat. AND you get a bonus. The class with Religion on the list ONLY gets a bonus. Basically, your background is worth
less, if you want to play a character with a class that is very close to his background.
I'd like it a lot more if they reduced the bonuses slightly, but give you an extra bonus if you already have it on your class list.
EDIT: This is even better illustrated with the last background - Imbuer. If you're wizard (for which the background is intended), you can create implements. If you're a warlock, you can create implements AND use Creation rituals.
So the intended classes get the least out of their background - that rubs me in the wrong way.
Cheers, LT.