To those who say "Nothing is real," I once replied, "That's great, but how does the nothing work?"
Suppose you learned, suddenly and definitively, that nothing is moral and nothing is right; that everything is permissible and nothing is forbidden.
Devastating news, to be sure—and no, I am not telling you this in real life. But suppose I did tell it to you. Suppose that, whatever you think is the basis of your moral philosophy, I convincingly tore it apart, and moreover showed you that nothing could fill its place. Suppose I proved that all utilities equaled zero.
I know that Your-Moral-Philosophy is as true and undisprovable as 2 + 2 = 4. But still, I ask that you do your best to perform the thought experiment, and concretely envision the possibilities even if they seem painful, or pointless, or logically incapable of any good reply.
Would you still tip cabdrivers? Would you cheat on your Significant Other? If a child lay fainted on the train tracks, would you still drag them off?
Would you still eat the same kinds of foods—or would you only eat the cheapest food, since there's no reason you should have fun—or would you eat very expensive food, since there's no reason you should save money for tomorrow?
Would you wear black and write gloomy poetry and denounce all altruists as fools? But there's no reason you should do that—it's just a cached thought.
Would you stay in bed because there was no reason to get up? What about when you finally got hungry and stumbled into the kitchen—what would you do after you were done eating?
Would you go on reading Overcoming Bias, and if not, what would you read instead? Would you still try to be rational, and if not, what would you think instead?
Close your eyes, take as long as necessary to answer:
What would you do, if nothing were right?
All I'm saying is that I believe that what morality actually is for each of us in our daily lives is a result of what worked for our ancestors, and that is all it is.
But if I understand you, you are saying that human morality is human and does not apply to all sentient beings. However, as long as all we are talking about and all we really deal with is humans, then there is no difference in practice between a morality that is specific to humans and a universal morality applicable to all sentient beings, and so the argument about universality seems academic, of no import at least until First Contact is achieved. In particular, a lot of moral non-realists are wrong. For example, those who think it is merely a matter of personal opinion are wrong. Those who think that it is relative to culture are wrong (at least for large chunks of it). Nihilists are wrong (insofar as they deny even the human-specific morality which you acknowledge). Those who think that democratic majorities define 'morality' are wrong. And so on.
As far as whether there are philosophical traditions which acknowledge or at least are compatible with the specificity of human morality to humans, I think there are. The natural law tradition ties law to morality and identifies a natural morality - a natural right and wrong. As the Stanford Encyclopedia of Philosophy describes it:
This leaves open the possibility that alien intelligences do not share our human nature and so are not bound by the precepts of (human) natural law.