Individuals can, and do, make their own decisions about what is moral. Some conform to generally accepted systems. Some don't.
As you say no society can exist in which all systems are given equal validity. So we have law - which is public morality. There is and always has been tension between the two. "Render unto Caesar..." is one way the tension has been resolved.
So far I think we are in agreement. Where we differ is that you feel a need for, and find evidence of, an objective morality - most probably religious in origin. I don't. Certainly we are all human beings and that places certain constraints on us but how, and in what detail, that translates to specific moral rules is, for me, far from definite and much subject to modification and experimentation.
And why would that be without some objective morality?
Not even close to being in agreement.
Individuals can, and do, make their own decisions about what is moral. Some conform to generally accepted systems. Some don't.
You missed the boat. Yes, people make moral choices daily - that's a no brainer. But they do not decide what is right and what is wrong. That has been decided. "Generally accepted systems" is a form a relativism wherein society decides - this is a form a relativism ("society says relativism"). The fact is that if individuals can decide what is right or wrong, then I cannot be wrong no matter what I do. Thus, if I kick you in the knee and steal all of your stuff, I am right because I say so, and under relativism's principles, you cannot object without contradicting your own bogus ethic.
By the same token, if I am Osama bin Laden, I could care less what American society says about what is right or wrong as muslim society dictates what is right or wrong for me. With this in mind, how do you adjudicate these differences between societies? - based on what universal principle that would apply to all? The Prime Directive? LOL. The answer is: Right and wrong come from God - there is no other answer.
You obviously have not worked out these problems yet.