Didonians are one intelligent species who are constitutionally incapable of believing that they possess immortal souls. They already know that each individual consciousness is transient and that it has three constituents that can be combined with others to form consciousnesses with overlapping memories. Anderson's Ythrians of the New Faith believe that what matters is how they die, not that anything happens afterwards.
One of Niven's and Pournelle's Moties says that some Moties believe in souls and that others do not:
"'Like humans, Moties do not care to think their lives are purposeless. Or that they can and will be terminated.'"
-Larry Niven and Jerry Pournelle, The Mote In God's Eye (London, 1979), p. 79.
I think we are told that, in one Motie religion, an individual's soul is divided between her descendants? (Addendum: This is confirmed on p. 493 but it had first been mentioned earlier.)
As I understand it, what happened in human religion was this -
(i) We seem to leave the body and sometimes meet (dream about) the dead temporarily in sleep - therefore permanently in death. However, souls in Hades, Hel or Sheol were merely conscious of not being alive. This lingering on was unpleasant but unavoidable.
(ii) When society divided into classes, social stratification was projected into the hereafter: warriors in Valhalla and drowned sailors in Aegir's hall but everyone else in Hel.
(iii) Rightings of wrongs and social reversals in the hereafter. Thus, a happy hereafter for the righteous was a third and later stage of ideas about survival after death.