You mention three moral issues here. Murder, theft and adultery. Out of these only murder seems to be a biologically driven taboo. Conjugal rights and even the whole concept of marriage seem to have evolved after the Agricultural revolution at the end of the neolithicum. There is evidence that in most hunter gatherer tribes, women simply chose their bedmates as it suited them. Polyamorism is of course an excellent way to achieve genetic diversity. 'Moral' codes seem to be usually laid down by tose in power to maintain the status quo, not driven by some genetic predisposition.
What, I believe, is biologically driven is the inclination toward cooperation and empathy, not its manifestation. How these tendencies are expressed in specific moral or legal precepts will vary from society to society and from time to time.
To the extent we are talking about "'moral' codes laid down by those in power to maintain the status quo," I think we are talking about law. While law and morality may overlap, and law is frequently dressed in moral or religious garb, the distinction is that the former is enforced by temporal coercion (jail, fines, execution, etc.), while the latter relies on something else, perhaps indoctrination or the promise and threat of rewards and punishments in the next life.
but who then to decide?
Depends on the society we are talking about. In a monarchy, it's the king, in a theocracy, the clerics, in a democracy, the rabble.
because what is right for you, can be wrong or even damaging to another.
Let's take an example from the recent months. the Trayvon Martin case. Was Zimmerman's shooting of martin a wanton killing, or a justified act of self defence? To decide that, we'd need a common understanding of what encompasses self defence, and what is considered justified.
Yes, we do need to reach a common understanding of when the use of force, especially deadly force, is justified. However, the question may be resolved in entirely utilitarian terms, rather than moral ones.
I think it self-evident that freeing people to blast away at each other under any but the most limited of circumstances is inimical to the social order which enables us to avoid lives which are nasty, brutish and short. The Florida "stand your ground" statute is bad law, in my view, because its license for violence where not absolutely necessary (i.e., where retreat is possible) brings us a step closer to chaos, and a step further from a world which allows the greatest number the opportunity to maximize their happiness and security.
Our government has laws based on a certain moral code laid down by an organised party. Now whether this is a religion, a state, or any other form of power doesn't really matter I think. Is there really a difference between loving someone because jesus said you should, or because a real person said you should.
Is there really a difference for killing because your pope wants the infidel dead, or because your president wants the infidel's oil?
Well, yes. In a secular democracy, and one which favors minimal government intrusion in private decision making, it makes all the difference in the world whether government acts out of secular considerations or religious ones (though, admittedly, the dead infidel may not care).
Though I realize the religious right would disagree, I think the founding fathers had in mind a government that would deal with problems of this world (regulating trade among the states, stealing land from native Americans, and what-not) to give us all the greatest advantage in our private pursuits of happiness. Conversely, I also think their intention was to leave individuals to strike their own bargains with higher powers. When government loses sight of the distinction, and proscribes rules because they are good for our souls rather than our bellies, it unnecessarily circumscribes the field of individual action (e.g., proscribing contraception, abortion, marijuana, smut, etc.).
We may disagree with our government that killing infidels for oil is a good thing, but at least if we are all on the same secular page, there is hope our elected representatives might be persuaded that their policies are not conducive to maximum happiness. The game is lost, however, if we need also persuade them of what God wants.