Of course Moses presents one concept of the law of God. Paul of Tarsus presents one that’s somewhat different. So does Mohammed. And Joseph Smith for that matter.
FWIW, I disagree with this statement, Notary.
I do not think that there is any difference between the Law of God set forth by Moses, and that set forth by Saint Paul -- only a difference in the Enforcement of those Laws.
In Romans 13:1-10, Saint Paul does quote the same Laws of God set forth by Moses, but he only delegates Gentile Civil Governments with the enforcement of the Second Table of the Ten Commandments -- the Civil Laws against Murder, Theft, Adultery and other Contract-breaking, Fraud, Abuse and Malfeasance (and that's it: that's the extent of Government's delegated authority). The First Table of the Ten Commandments, the Religious Laws (against Idolatry, Blasphemy, Sabbath-breaking, etc.) Saint Paul does not delegate to the Civil Magistrate, instead leaving the proclamation of these Laws to the officers of the Church.
So the Law of God has not changed since the Theocracy of Israel; it's just that, under the New Covenant, Gentile Civil Governments are only charged with the enforcement of the Civil Laws of God, not the Religious Laws.
Ah, but in a dramatic demonstration of natural law all of the religions you cite agree that the taking of innocent human life is murder. The jihadis excuse themselves for killing civilians because they categorize them as “not innocent.” Naturally, that is deeply flawed reasoning, but on the core premise there is still agreement. That is the basis of natural law, that there are discoverable universal moral axioms, and our constitution is wrapped around three of the big ones, life, liberty, and property. Our founders did not and would not accept as valid the rule of any government that fails its people in regard to those three great natural law axioms.
It may be disagreeable to some that these axioms were “discovered” in the context of western religious traditions, but that is historical fact. Better it is to judge those axioms by the good fruit they have yielded, and to reject any interpretation of federalism which tends to their destruction, especially when the founders, who invented American federalism, can be shown to have based their entire project on those same axioms.