The problem is that I (and probably most posters on this thread) am not a neurologist or on the cutting edge of evolutionary studies, so the complex questions and answers about which genes affect morality and how they work go unanswered. But I think there's a danger of concluding ha, I stumped them. They can't answer my questions so therefore they're wrong.
I hope I didn't sound like I was doing that. What I'm saying is that I don't find evolutionary or biological rationales for behavior particularly compelling. Not because we aren't grounded in biology, and not because behavior is something special that escapes materialism, but only because we have much better descriptions at higher levels.
A strong parallel would be trying to describe biology with quantum physics. We probably all agree that biology is subject to the laws of particle physics, but quantum mechanics just doesn't capture (or explain) what interests us.
So I'll speak in vague terms because that's all I know, but I think there are many competing "morals" encoded in any human. Following rules is good because it stabilizes the group and avoids endless arguments, and reliance primarily on that trait might create a conservative. Sympathy for the poor is good because it allows more group members to survive, many of whom in a small tribe might carry some of your genes, and reliance primarily on that trait might create a liberal.
Some changes are so small I don't think they even count on the evolutionary scale. Vegetarianism based on sympathy for similar creatures may come from caring about humans in our tribe, but we have the luxury now to spread it out to larger animals. I don't know of any hunter-gatherer tribe that is vegetarian by choice, but no evolutionary-scale change is necessary for empathy as a trait to be more dominant when agriculture provides plenty of vegetables all year.
I think all these competing but individually useful morals are encoded in us, and each individual relies more on some than others. Nature? Nurture encouraging some traits? Probably both, but to get it down to the genetic level requires somebody far above my pay grade.
The difficulty I see is in the "flavor" of the evolutionary explanation, what I'm calling a pseudo-explanation. We find some trait that strikes us as noteworthy, and then try to figure out how that trait might have evolved. This is generally based on the utility we ascribe to the behavior that has our attention.
Sounds good so far, but "sounds good" isn't enough. "Sounds good" is fine for myth making and "Just So" stories, but if we want to take the subject seriously, we need evidence. That's hard to come by with something that doesn't leave fossil evidence.
There's also the danger of thinking the traits we like or find useful are somehow justified by evolution - they are better because they survived. We become the puddle, thinking the current situation was the outcome of a directed process. But it doesn't have to be. And, so far as I know, there's no way to prove the just-so stories false.
For morality, it's even worse. We can say that being moral goes along with being social animals. Alternatively, we could say we are social animals because we are moral. Or, we could say morality is simply an accident that springs from cognition and theorizing about others.
To distinguish the variants we'd need to run experiments. But we only have the one-off historical experiment to look at. In my view, there simply isn't enough data to be had.
There's a really good, free course out of Stanford on "Human Behavioral Biology." The whole lecture series is good, but the second and third lectures address these issues directly.
https://www.youtube.com/watch?v=Y0Oa4Lp5fLE&list=PL848F2368C90DDC3D&index=2