Lore-wise, changing race is possible in Destiny. Cayde-6, which you know is an Exo, was formerly a human according to the lore. And at one point in Destiny 2, your ghost says that the Awoken "are converted", meaning that the Awoken could have been something else before becoming Awoken. I don't know about changing from Exo-to-Human or Exo-to-Awoken though.