Similar, but thankfully a whole lot less of a pressing issue. I know that in Catholic doctrine, the idea that human beings, even they evolved, must have been ensouled is basically no stricter than “at some point before the rise of language and civilization.” Basically, it doesn’t matter exactly when (like it does in the abortion debate) because it’s already thought to have happened no matter what, so we need never deal with it as a real problem we face today (since everyone supposedly already has souls now.)
Michael Shermer raises some interesting questions about this, pointing out as he does that no particular instance of you is really “you” nor is a sort of conglomeration of all the yous that have ever existed. Right now, at this very moment, the “me’s” of several years ago are gone, and even if my death now continues on in an afterlife, that does nothing to change the fact. What if I was a really nice guy when I was younger, but then I contracted a mental illness and became a raving ass? Which “me” would survive into the afterlife? Both are “me” in a real sense, yet neither are complete. If I just continue on, then the younger me is just as dead forever as the older me would be if there was no afterlife.