Simple the Elves are immigrants to Faerun, so are the Dwarves, Gnomes, Mindflayers, Orcs, Gobliniods, Halflings.
The original races of the Forgotten Realms were the Creator Races and the Giants (with Dragons coming later).
The Creator races are the Sarruhk (reptilian race that created Yuant Ti, Coults, forgetLizardfolk, Pterafolk, Nagas), anBatrachi (an Ampbian race that Created the Bullywogs, Doppelgangers, Tako, maybe the Fund too), a Bird race whose name I forget (they created the Aarcrokas, Kenku, Dire Forbid races), and the Leshay (Fey Creator race who created a bunch of Fey races, but not elves). Humans were a creator race as well.
So almost every race in the Forgotten Realms is either one of the Creator Races or one of their/descendants, an Immigrate Race, a creation of a Wizards experiments, or really minor race that has had only minor impact on history.
So many of the older Faerun Gods weren't always primarily worshipped by humans originally, for example Sseth, Jazran, Mkshulk, and a few others are really independent aspects of a God worshipped by the Reptilian races called the World Serpent, who was very much not a human friendly God, the Batrachi have their own Gods, and so on, but as these races mostly died off, humanity Gods ascended to the spotlight.
Some if the Creator races may have worshipped Shar and Selune as well, or honoured them in some way.
So most of the Mythology of the Dwarves, Elves, Orcs, and so on don't come from Faerun, but from before, with some exceptions such as the Orcgate Wars, the Creation of Evermeet.
Actually the Elves probably had the biggest impact on Faerun of race, even though they are immigrants, because of the Sundering ritual which created Evermeet causes ripples through time, backwards and forwards, trigger the current Sundering, and the Sundering in the past, where the Batrachi Empires largely ended, and Abier and Toril where first split in two.
And some humans do worship none human deities, for example Mordin. I think it's more common amung the big name racial Gods, but it's still rare.