Can't you imagine lots of differents effect on the gameplay ?
Specific skills or spells ?
Specific side quest or way to resolve some of them ?
Specific interractions/reactions, gifts, support on your story ?
I don't know... I'm not the best to say what is D&D lore but you can imagine many things...
I personnaly don't care about deity but I can't imagine someone is "against" the concept in a ROLE PLAYING game.
It looks role play and story telling is not intterressants for the "modern" consumers.
Was this a reply to my post by any chance?