It is worth considering your model for deities as to whether this would be a good change.
The current model of deities in Forgotten Realms, in most D&D worlds for that matter, is a model where mortals can gain significant power and slay deities and take their place. In such a world, it probably wouldn't make sense to posit that only humans have the time and the drive to gather so much power. Surely the longer-lived races would be more prone to having this occur.
Granted, most racial deities, at least the ones initially pointed to, are the fathers or mothers of whole races and have been around for longer than their entire race rather than the kind that are champions of their race that rose to prominence, so that does undermine it a bit. If there are instances of mortals rising up to slay gods, even multiple instances within a 100 year span of time, are we really to believe so many racial founders-- particularly those antagonistic towards the peoples who can ascend-- would still be standing after 10,000 years?
Granted, I suppose you could add a caveat that whatever it requires to ascend to godhood requires one to give up racial definitions as matter-of-course and people tend to forget from what people the mortal once came from... though it seems a bit incredulous that people would recall a heroes stories and actions without recalling their defining characteristics.
Of course, you can throw out that model. You can say that no mortal can ascend to godhood, but rather the deities are something special and unique from the very beginning when they come into being-- usually from older deities' powers somehow coming into contact and resulting in a new, generally more focused cosmic force. You would have to change a lot of the history of the land, or at least say that the history as presented didn't really happen that way and it was a complete fiction with deities just not expressing themselves to mortals in clear enough term for these false stories to be overturned.
But, if you did use this model, you could probably get away with saying that a number of the deities are just the same one as worshipped through the lense of different cultures. The real deities would be racal-neutral with numerous names. It could even be that some of the deities thought to be enemies of one another are actually one and the same. Again though, this would mean it is necessary for deities to somehow be unable to interact with followers in a direct and detailed enough manner to clear up the misconceptions... or possibly to somehow benefit from the conflict.
Of course, even if you were to do that, it doesn't preclude the possibility that one deity was chiefly responsible for shaping a particular race to be different from the others and thus it would still be their chief deity. Talos and Gruumish being one and the same or Tyr and Maglibiyet being the same would just mean that Orcs primarily worship Talos and Goblins primarily worship Tyr and probably their image would be so closely linked that Talos would be generally portrayed as an Orc and Tyr would be primarily portrayed as a Hobgoblin. Granted, it would mean that there are worshippers of these deities that are not the primarily race they are associated with-- so that is something-- whether that means that followers of the same deity can reach beyond racial lines to join together more easily or if they conflict bitterly over interpretations of the doctrine are up to you.