Morality can't be for all, because the laws that we follow are recommendations, for our species to survive in a civilization. A dictum to not eat pork, or wash your hands, might be to control infection. You can argue that monogamy or permanent polygamy is also to control, or slow venereal disease, rather than the wrath of God. Obviously, killing is not good for our species, or any mammal, because our reproduction times are very slow, and the investment per child is high.
If the species changes, then the rules change. If you have a species which requires fertilization from multiple males, then you cannot possibly have monogamous morality, or the species will die. If there are no venereal diseases, then you can screw who you like. If the species requires rape to make the female ovulate, then rape is moral. If the animal requires death to spawn, then killing in certain circumstances is moral.
Morality is what necessarily has to happen to make the species survive, or the civilization/culture flourish.
It follows that God cannot have any morality, unless you know what God is trying to achieve, because the morality of God will be convergent on what needs to happen, for his reproduction to occur. We have no information on what God needs, to reproduce, or who he needs to exploit to achieve it. God could have no morality at all, if he does not need to reproduce, or create culture.