Cultural historians studying the history of religion and belief systems trace how religious institutions, practices and ideas actually shaped politics, law, art and everyday life across different societies and centuries. That project is genuinely different from theology, which asks whether a religion's specific doctrinal claims are actually true, a historian studying, say, how the medieval Catholic Church's landholdings shaped European feudal politics is doing history regardless of what they personally believe about Catholic doctrine.
Historical study brackets the truth question entirely and studies function and influence instead
A cultural historian's central questions are about institutions and effects: how did a religious authority acquire and use political power, how did religious law shape secular law, how did religious patronage shape which art and architecture got built and preserved, how did religious calendars and rituals structure ordinary people's daily and yearly lives. None of those questions require settling whether the religion's own claims about the world are correct, which is precisely what lets historians of religion study traditions they don't personally practise, or don't believe, with the same rigour they'd apply to any other historical institution.
Religious change itself gets explained through the same historical, not purely theological, lens
Major religious historical events, conversions, reformations, schisms, religious wars, get analysed by historians as processes shaped by political, social and economic pressures running alongside genuine belief, not purely as the record of doctrinal disputes settled on their own terms. A king's conversion to a new religion, for instance, gets studied for its political consequences, alliances gained or lost, land and authority claimed, just as carefully as for whatever the king's own stated religious reasoning was.
What we're still unsure about
That cultural history of religion studies institutions and social effects rather than doctrinal truth is a well established, uncontroversial methodological starting point in the field. What's more genuinely a matter of ongoing historical debate is how much weight to give genuine religious conviction, as opposed to political or economic motive, in explaining specific major religious historical events, historians are generally wary of purely cynical explanations that reduce every conversion or reform to naked self-interest, and equally wary of purely idealist explanations that ignore obvious political stakes, and where any specific event actually sits between those two poles remains genuinely contested case by case.
This sits inside The History of Religion & Belief Systems, one of seven topics in Cultural History, one of seven domains in History, one of seventeen subjects the app can quiz you on.