All characters should have the option of choosing a diety, part of the PHB!
Being or not being part of PHB is not really the important question ...
Important question here is if all characters should have deity-related option in dialogues ... or if that should remain for Clerics only!
I mean ... Give it to everyone ... and Clerics loose lots of their identity. But keep it for Clerics only ... and there is no reason to implement it at all, since you will never be able to express your faith anyway ... so all you need to do is simply name your character Tav, worshipper of *insert deity here*.
Why would a random person who worships a deity be on speaking terms with the god at the same level as a devotee like a cleric?
Worshipping a god isn't the same thing as serving it.
