The main issue with not worshipping a deity in Forgotten Realms is that when you die, you are done for. Your soul goes to the Wall of the Faithless, to either be claimed by demons or devils eventually (in the bad way) or to just slowly assimilate into the wall and go into oblivion.
While the No Deity option should maybe be possible, it also would mean that when you die, it is game over because your soul is stuck in the Wall and you cannot be raised from the dead or resurrected. Even Revivify would not work and there is little the gods themselves can do either.
