May a modern civil magistrate govern according to Old Testament Law? Please explain your answer.
It depends on where you are talking about.
In the Americas or Western Europe, no.
There are several reasons why not. I will begin with the practical and political, and then move to the spiritual.
Magistrates are judicial officials granted authority by governments. The governments of the Americas and Western Europe are civil republics or constitutional monarchies. Even the most oppressive government in the region - Cuba - is a republic whose government was determined by a popular revolution.
America's and France's and Britain's governments were established by popular revolutions (the English eventually restored their monarchy but never restored its power). These are popular republics (in everything but name for the British), and the people of these countries - which are the dominant source of modern Western civilization - do not have any desire to live under theocracy. There is no mechanism by which a "magistrate" could arise with the authority to govern according to Old Testament Law. Magistrates in Western democracies are chosen by the people directly or by other public officials to fulfill a specific, limited function, with their authority exclusively derived from the civil law by which their office is instituted. They have no personal or individual authority to step outside of their job description and claim power to command the armies, declare war on Poland, order the tides back...or start enforcing some DIFFERENT law. The Old Testament Law is a DIFFERENT law from the law under which the magistrate is appointed. He has no authority to enforce any other law other than the one under which his entire authority itself derives.
Should an American, French or British (or any of the other little countries in their Western orbit) try to do so, he would not actually be enforcing Old Testament Law, because nobody would obey him. He would, rather, be declared to have gone ultra vires (beyond his powers) and be removed from the bench.
It is theologically wrong to quote Saint Paul as though he has the same authority as Jesus or YHWH - he does not - but it's childish to expect to to wield some sentence of some letter of St. Paul as a mandate in modern government to do anything. There will no doubt be a handful of loons who agree with the fellow who does so, but the whole Christian establishment, across the spectrum from Catholic to Baptist, will utterly reject the argument.
We live in a democratic republic. We have decided what our laws will be. Many of them are inspired by Biblical ideas, to be sure, but they are interpreted as we, as a society, have decided they are to be interpreted and applied - or not applied - through our elected government and our civil judiciary.
Any magistrate who sits on a bench anywhere who decides that he, spontaneously of his own authority, now has the right to start applying some DIFFERENT law other than the laws duly enacted by our country, has gone out of his mind. HE may decide that he has the "right", but he will no have the power, because he will no longer be a magistrate the day he starts doing that.
The writers of the Old Testament do not determine law enforcement of the Western World. We the people do. If anybody pretends otherwise, it is a pretense that will be met by laughter, at best. If anybody goes off his rocker enough to try to actually enforce his own will on the matter, as magistrates and judges occasionally have from time to time, usually in their old age, they are very swiftly removed from the bench and their decisions are null from the start.
God never intervenes to support them either, because theologically they would be wrong.
The law of the Old Testament consists of three major parts: A brief directive law to reproduce and eat plants and fill the world, given to the species at creation, a revision to that law permitting the eating of meat but prohibiting human bloodshed that was given to Noah and all of mankind after the Flood, and then the Law of Sinai, given by YHWH to Moses and the Hebrews of the Exodus.
Only the first two of those laws ever applied to anybody but the Hebrews.
Leaving aside democratic and pragmatic realities, it is theologically wrong for anybody to hold up the Law of Sinai and claim that that is the law for the world, or that it EVER was. It NEVER was. Not ever. All it is, or ever was, by its own literal terms (to those who bother to read it carefully - few do) is a contract between two parties: YHWH, and the Hebrews assembled at Mt Sinai. The terms of the contract are thus: IF you Hebrews do all of these things in the land of Canaan I will be giving you, then I will give you a secure farm there. And if you don't do them, I will take back that security.
That is it. That is all. There is nothing more to that law. No matter how many emotional claims are made otherwise, it is not a law for the world.
There is never any promise of, nor even MENTION of, life after death, eternal life, final judgement - anything after life at all - in the Old Testament Law. It's entire focus is THIS life, and the only promise is a literal, physical farm, in peace, in the land of Canaan, in this life, for the Hebrews hearing the covenant, and their circumcised lineal heirs who kept the whole law.
The Old Testament does not tell men "how to go to Heaven". In fact, it doesn't ever say that men ever go TO Heaven. The dead in the OT go into the ground, down to Sheol, and stay there, as shades. That's the end of it. A handful of prophetic statements towards the end of the OT suggest otherwise, maybe, but none of that is the Old Testament Law. The Law is found entirely in the Torah.
Essentially, a magistrate who started to enforce the Old Testament Law would be a madman who was violating his oath of office in pursuit of a religious belief that would be an idiotic form of heresy. He would be stricken from the bench as soon as he stared doing so, his judgments would be nullified, no credible Christians or Jews would support his efforts, and neither would God. He would have completely misread the law of his own land AND the Torah, and should be nowhere near a seat of judgment, as he would lack any.