There are a few things to unpack here.

One is that the concept of religion as an identity in and of itself, and as a matter predominantly of personal belief, is to some extent a product of a world heavily influenced by Christianity. In antiquity, the gods you worshiped and the rites you participated in did not depend on personal conviction as much as where you lived, and what your ethnicity was. Gods were said to be associated most strongly with the physical locations in which they were worshiped, or with the particular ethnic/tribal group they protected. Athens was strongly associated with the worship of Athena, just as Ephesus was with the worship of Artemis, and the god of Israel in the Old Testament was just that: the god of the nation of Israel. Other groups had their own deities, and in some cultures, such as Rome, individual households had their own gods. The practice of religion was an important marker for one's membership in an ethnic/cultural group or city, and the proper observance of sacrifices, feasts, and rites was a critical function of the state. Refusing to participate in the religious practices of your city was tantamount to disloyalty and removing yourself from your extended kin group. This is one of the reasons why Christianity was controversial: it was a universal faith that had no ethnic loyalty. To practice Christianity, then, was to jeopardize one's loyalty to one's city and family. Because Christianity requires that its believers not worship any other gods, Christians had to abstain from civic and family rituals that were once essentially mandatory. Jews sort of got away with this precisely because of the ethnic component: even if Jewish practice seemed odd to pagans, this was just the way that people of Jewish descent practiced their faith. One of the earliest charges leveled against, Christians, incidentally, is that they were atheists. This was not in the sense that they did not believe in any gods, but in the sense that they did not obey the religion of the state by refusing to sacrifice to the genius of the emperor, and so forth. In a world in which people seriously believed that angering the gods had serious consequences, keeping the gods happy was a matter of public policy. Religion was not a private affair, it was inherently public.

Additionally, through much of human history, kings and rulers have been thought to have a special relationship with the almighty. In some societies - pharaonic Egypt being a main example - they were seen to literally be gods. When they were not seen to be literal gods, they were often believed to be descendants of gods, or have certain priestly functions. In certain cultures, kings enjoyed a unique intercessory power before the almighty, as well as a unique accountability. The extent of this phenomenon - called "sacral kingship" in the literature - has become more controversial in recent years, but it has definitely existed in certain cultures. Keeping god, or the gods, happy was the unique province of kings. What this also meant was that matters of religion were matters for the king. The king's god was the god of his people. When kings converted, for whatever reason they chose to do so, many of their people went with them because they keenly understood this sacral relationship between the king and the heavens. This doesn't mean they never got pushback, but kings were responsible for dealing with things supernatural, so when kings "converted," many others followed. This didn't mean that people didn't continue partaking in certain pre-Christian observances on the side, but it did make whatever form of Christianity had been adopted - frequently Arianism during the Migration Period - became the new official cult of the people.

This can also work in the other direction. Henry IV of France, who started out Protestant, is said to have concluded that Paris was worth a mass, and submitted to Rome. Whether or not he actually said this being beside the point, it very much mattered by that point what type of worship the king was engaged in. Even well into the early modern period, French kings, and to some extent English kings, were still thought to have a unique relationship with the divine. This is the explanation for the persistence of the practice of “royal touch” by which kings were said to be able to heal skin diseases by touching the afflicted. The problem for Henry was that he had been very publicly Protestant in a realm divided by religion, and that had been accustomed to Catholic rulership. Like English coronations, French coronations included an anointing, or unction, in a quasi-ordination like ritual that in France was next to impossible to participate in if one was not Roman Catholic. At certain points in history, the act of unction itself was even seen as in and of itself constitutive: upon unction, the person anointed acquired certain mystical, charismatic qualities only a king could possess. Many of Henry’s devout Catholic subjects genuinely believed that a king could only truly rule France if he were a Roman Catholic, and that that the religious rites associated with kingship would have no effect on somebody who was not. We can think this is silly if we want, but people genuinely seemed to have believed this.

This is all a long way of saying that people throughout history have approached the notions of religion and rulership in ways very different from our own. People did not necessarily swallow uncritically everything they were told, but ideas about religion and governance were closely interlinked in a context that I think would be very foreign to us today.

Readings

Ronald Asch, Sacral Kingship Between Disenchantment and Re-enchantment: The French and English Monarchies, 1587 – 1688

William Chaney, The Cult of Kingship in Anglo-Saxon England

Robin Lane Fox, Pagans and Christians

Larry Hurtado, Destroyer of the Gods: Early Christian Distinctiveness in the Roman World

Francis Oakley, Empty Bottles of Gentilism: Kingship and the Divine in Late Antiquity and the Early Middle Ages (to 1050)

Francis Oakley, Kingship: The Politics of Enchantment