I completely agree. Would help a lot with immersion and give out character some kind of alignment based on which deity they worship. It could provide interesting dialogue branches and even affect those short scenes we get when alone at camp. Maybe our character could pray or ask for their god's blessing/express their doubts to them and ask for advice. Even if no answer comes, it's a good chance to give custom characters a bit more depth.
1+ for this suggestion. I would like everyone to be able to choose the deity they profess (or lack thereof) when creating a character, even if the plot and mechanics would not change anything (although it would be great to be able to do some activities related to the deity or have additional dialogue options). After all, when we choose a character's appearance, it doesn't really matter much either. As far as I know, if I create a character with pink hair and brown skin no NPC will comment on it, but I will do it anyway because I want to, because it helps me feel better about my character. It should be the same with the deity. Whether I'm a priest or a thief, I want to be able to choose a god and at least imagine my character praying to him. And if I decide to play a male drow who, after a bad experience with the priestesses of Lolth, is fed up with gods and refuses to worship any, then I wish to be able to do so.
I really liked that NwN2 had so many different gods to choose from for each class, even though they had virtually no meaning in the game. There was even a Gargauth about which little was written in Player's Handbook 3e. I wish Baldur's Gate 3 also had so many deities to choose from + Archdevils and Demon Lords.