Some things that come to mind for me are:
1) Original Sin. Without this story, how would we come to think that a sin nature passes through generational lines? Or that there was ‘original sin’ at all?
1a) …thus, infant baptism would probably not be taught/understood/practiced.
2) What would be our reasons for Jesus having to die for us if we didn’t have the “first Adam” story and its lessons?
3) Marriage. Would we just be missing one argument about “man and woman only” or would a larger definition of marriage change?
4) Satan: what would our beliefs about evil be like?
5) Would we really understand sin? How would our theology on sin look without it?
Basically, I’m really curious about how much we derive from a story, a myth. when I really get thinking about it, so much of Christian theology and doctrine has been formed out of this tale.