Is the Bible True?, page-474

As a matter of fact the Jews had a theocracy, but those of different religions were tolerated within it.

The unity of church and state was common in ancient times.

Most of the ancient peoples had survived within governments dominated by other religious persuasions.

The persecution and slaughter of minorities occurred from time to time, but the records show that peaceful coexistence was more the norm, and intense hostile preoccupation with the religion or ethnicity of others was fairly uncommon, though naturally the conflicts tend to be noticed more. Some religions had practices so repugnant that they engendered real avaersion, such as the Baalists who believed in child sacrifice; but even there the tendency was towards accommodation.

The issue in a theocracy is how religious minorities are treated, and whether they have appropriate freedom to practice their beliefs.
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At the time of Jesus' life, the Romans had been invited into a civil conflict between competing factions, to the later regret of the Jewish nation; and also at the time of Jesus, there was acrimonious differences in opinion among the Jews as to what to do about it. Once the Romans got in, the Jews were unable to get them to leave, and there were violent disagreements in the Jewish leadership about what to do about it.That is why Jesus was a target: the Romans were fearful of a populist Jew who potentially had the ability to lead a major revolt, should he have been so inclined. And the Jewish establishment had no use for Jesus either,
as he was openly critical of them; and they were responsible to the Romans to keep their people in civil order.

It is interesting that at the time of Jesus, there were tens of thousands of Jews living peaceably in Rome under Roman civil authority; and there does not seem to be any record of serious problems from them in Rome, even during the murderous war in Israel that saw the deaths of a large part of the Jewish population there.
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A thousand years earlier King Solomon ruled the Jewish kingdom and was so tolerant of other religious groups (especially their women) that it was considered to be his major fault by the authors of the Old Testament. Besides taking many wives from other religions, he encouraged them to build temples to their gods, in Jerusalem.

The problems with theocracies seems to come about when there is the need to proselytize and convert others.

Islam and Roman Catholicism appear to have the worst record on this.

For the most part, the history of the ancient world shows many groups living in close proximity without problems.

The wars that occur do not seem to be wars of religion, though naturally the combatants usually had different religions.

But religion was not the cause.

They seem mostly to occur from the egotistical megalomania of the leaders, and their desires for wealth, fame, and power.

Alexander the Great did not conquer the known world for religious reasons.

Nebuchadnezzar did not invade other nations to convert them to his religion.

The Romans did not care what religion their conquered peoples had, as long as they paid tribute.

When it comes to separation of Church and State, we could learn a little from the ancients.