Empathy is an innate feature in humans (not that it doesn't exist in other animals.) The ability to model other minds in a fairly complex way, and thus to hold justified nth-order beliefs, is pretty clearly adaptive - you couldn't survive in a complex social group like the ones humans form without it. The way in which it does so inclines us to be more altruistic - although we also have the ability to accept social programming that selectively turns off our empathy - but I see no evidence that that's not a spandrel.
Morality is necessarily a social construct, although the emotions that define it as a category - admiration, contempt, shame-or-guilt, &c. - seem reasonably universal. (Although see the wonky need to group shame and guilt together to say that.) The most people can say about the universality of morality is that "every society condemns theft and murder," which is a tautology.
Probably any social group of beings with reason, empathy, and the propensity to adopt social conventions as a heuristic would have something like morality; these and historical factors, I think, are enough to explain the diversity of moralities that have existed. An evo psychic explanation as such would require recourse to massive modularity, and while possible, that would be an unnecessary multiplication of entities. (In general, ep explanations have this quality: very rarely is there an evolutionary story for a behavior that is not also an explanation for why a rational being would not adopt the behavior as well.)
Questions of its truth or justification aside, the ideological problem with ep from a left perspective shouldn't be that it presents a vision of homo economicus. (We're the ones, after all, who believe in economic explanations.) Rather, the ideological challenge is that it presents us as (i) irredeemably *irrational* and not psychologically suited to our present material conditions, and (ii) unequal by nature. (Back when it was called sociobiology it was happy to speculate about race; now, ep has the tact to restrict itself to sex.)