The rebirth issue would be bigger than the biological one. Purely natural ex nihilo creation has always been the theist argument most compelling to me; otherwise I tend to endorse the view that natural laws were devised so that the universe doesn't need constant micromanaging. Setting aside how I feel about this statement itself, I find the notion of endless transmigration implausible, if only because of sustainable issues.

A biological origin for souls would be unexpected in the sense of giving a physical analog to something generally understood as spiritual, but Christians obviously believe the spiritual can produce the physical, and a biological origin for souls is just as obviously not an origin for existence. Thus I'd still be left with a choice between ex nihilo creation or a supernatural First Cause of the natural universe; no change there. If you treat transmigration to mean brain death isn't actual death (since the souls life could continue) it's not hard to reconcile with core Christian doctrine (obviously the more beliefs you add to that core the more controversy is likely) so that wouldn't change much in itself either. The end game, if any, is what's relevant. Spirituality aside, the First and Second Law of Thermodynamics don't lend themselves to things like Big Bounces or ex nihilo creation. Even if souls were found to be tangential to or entirely irrelevant to those issues the issues themselves would remain. It might, however, convince some people to change religions if they couldn't see a way to reconcile the new findings with their current religion.

Welcome.