I'm dubious of any moral claim, such as valuing vegetarianism or celibacy, that requires people to act contrary to their natures in a way that decreases their fitness.

Genetic fitness matters, because a moral system must be evolutionarily stable.

This implies that tragedies of the commons are acceptable under such moral system.

(Under the "tragedy of the commons" I mean a situation where "selfish" members of a population take advantage of a communally-maintained resource while not contributing to it, thus gaining free energy to outreproduce the "good citizens", thereby increasing the frequency of the genes for cheating and reducing the frequency of the genes for maintenance of the common resource. Any population consisting only of "good citizens" is evolutionarily unstable because it is vulnerable to an invasion of "selfish" mutations.)

Thanks for the clarification. I think I have a somewhat clearer idea what you're getting at now, but the distinction you are attempting to draw between ethics and goal attainment still seems wrongheaded to me. As the designer of a posthuman society, your ethics determine your goals; I don't see how the two are supposed to come into conflict in the way you suggest. (Maybe the demands of evolution will place constraints on the psychologies of feasible post-humans, but that's a rather different point.)

Nitpick:

An individual human can reason about it, and choose a different valuation; but they're then trying to act in a way inconsistent with their psychology

As it's currently stated, I don't think this claim makes any sense. If they can do it, then it's consistent with their psychology.

Why must a moral system be evolutionarily stable?

I'm dubious of any moral claim, such as valuing vegetarianism or celibacy, that requires people to act contrary to their natures in a way that decreases their fitness. [...] but when you then conclude that lions are evil for eating zebras, you've gone wrong somehow. I don't buy the argument that the rules are different for humans because they can reflect on the rules.

(Emphases mine). Please settle on a set of applicable subjects. I'm with you that moral claims apply to "people". I don't think many here will claim that humans exhaust that space in theory, or that lions inhabit it currently.

This does help clarify things. Unfortunately, Conchis is right, you're committing the naturalistic fallacy.