As for those moral precepts which are common to all cultures, if there are any, they are determined by observation and comparison...and there origin is most likely to be found in genetics.
To me your claims of morality originating in the supernatural are just so much superstition.
So which is it? Are you defending a morality -- if we can call it that -- which is "never absolute", or one deduced from basic axioms?
As for those moral precepts which are common to all cultures, if there are any, they are determined by observation and comparison...and there origin is most likely to be found in genetics.
However, the violation of them must also be part of the range of human behavior you mentioned earlier. Otherwise why have a moral precept? If humans are truly genetically bound not to do something, morality doesn't enter the picture. The genetics in question can only be an inclination to become angry when others do it. But why should I care if it makes others angry? Because I'm afraid they might be angry enough to hurt me?