Bulverism versus Aristotelian analytics

I've noticed that many of the questions posted here are from Christians seemingly loading or begging a question (petitio principii) where they assume the inerrancy of the Bible and that any potential argument against it must be demonstrably fallacious. Invariably, their questions are innocently (deceptively?) framed and sincere enough, but then piled on with either more dogma or further paralogical (Strawman) assumptions. They pose the same question over and over again (Repetition fallacy) in variant forms as an excuse to proselytize rather than correctly identify the fallacy in their own thinking or another's.

The Bible is infallible and supremely logical, therefore any argument against it must be logically fallacious and false.

Now, in Aristotle's Analytics, the onus is on the "arguer" to correctly identify and deconstruct the logical fallacy of a premise or question before even attempting to argue the logic. In fact, he seems to suggest a circularly reasoned premise can be readily dismissed prima facie, and that one only errs further by failing to identify it upfront and risk being tricked into answering it. In other words, a logician is under no obligation to argue the logic of a loaded or begged question, as if to apply Hitchens and Sagan's maxim: "Anything introduced without evidence can be dismissed without evidence."

So, in this particular context, at what point does the deconstruction and identification of a fallacy in itself become an exercise in Bulverism?

"Bulverism: This is a combination of circular reasoning and the genetic fallacy. It is the assumption and assertion that an argument is flawed or false because of the arguer's suspected motives, social identity, or other characteristic associated with the arguer's identity."

Imagine if 80% of a certain gang were convicted murders. Billy was a member of that gang. Would it be wrong to assume he was a murder? It depends who you ask. I work off of probabilities. It is more probable that Billy is a murder than not (not having any other information). But I would never insist that Billy was a murderer based on probability alone. Likewise, when dealing with arguments, we can have our suspicions to the veracity of the argument based on some superficial information about the person making the argument. We just need to be sure that the stereotypes are accurate. Can we dismiss an argument from a flat-earther without investigating and researching it? I would. The "identity" is a strong enough warning for me to know not to waste my time. If I said the flat-earther was wrong about a claim simple because he is a flat-earther, then I would in trouble. It takes no more effort for me to say that the flat-earther is very likely incorrect, and I choose not to invest my time researching his/her claim.