What standards guide this questioning process? Will not those very standards be brought into question when the historical investigation abuts the grounds for religious belief? For instance, we doubt Herodotus’ stories about divine interventions at the Battle of Salamis precisely because historical inquiry is guided by a naturalistic heuristic just as much as natural science is. But won’t religious apologists complain that such reliance on “post-Enlightenment” historiographic standards bias the case against them?
This complaint conflates a default assumption with an invincible conviction. Initial skepticism, even very deep skepticism, about miraculous events, is not a problem unless the skepticism becomes dogmatism that refuses to consider the evidence. Apologists have no grounds for complaining that the job of convincing the rational skeptic is hard and that they have a lot of work to do. They willingly took on a tough job and they cannot reasonably complain that it is tough. It is not reasonable to ask historians to suspend the rules that they apply to all other inquiries as soon as the investigation turns to Christian claims. To do so would be a gross case of special pleading on the part of the apologists.
i) Parsons is less than clear about what he means. Apparently he's alleging that Christian apologists operate with a "naturalistic heuristic" for everything except Christian miracles. If so, on what basis does he say that? Does he think all Christian apologists automatically discount reported miracles in non-Christian settings? What about Christian apologists who believe in occult powers? Pagan witchcraft?
ii) The reason to doubt Herodotus’ stories about divine interventions at the Battle of Salamis needn't be based on a general, default naturalistic heuristic. Rather, we can doubt (or deny it) for the specific rationale that we have no reason to believe the gods of the Greek pantheon ever existed. Indeed, we have reason to believe they don't exist. Never did. It's not about "divine intervention" in general, but intervention attributed to the gods and goddesses of Greek mythology. If we have good reason to believe they do not exist–indeed, that entities like that cannot exist–then that's a specific rationale for doubting (or denying) Herodotus’ stories about divine interventions at the Battle of Salamis, which has nothing to do with methodological atheism.
iii) And, yes, "initial, or even very deep skepticism" about miraculous events is a problem because it's prejudicial. That can't be justified on a "naturalistic heuristic". That can only be justified if there's a solid argument for metaphysical naturalism. For unless you already know, or have good reason to believe we live in a kind of world where divine interventions don't happen, initial skepticism, much less very keep skepticism, is question-begging.