...Without Using Your Worldview to Support Your Claims

I see the following exchange archetype often these days:

Person A: I don't support Position X.

Person B: Why don't you support  Position X? Give me reasons, without using religion/a holy book or morality.

This is such an intellectually dishonest demand to make in a discussion. Basically, what it means is "I'm going to use my worldview when defending my position, but you are not allowed to use your worldview when defending your position." It's a blanket assertion on the part of Person B that their worldview is automatically superior or correct, while Person A's worldview is automatically inferior or incorrect. Hilariously (and frustratingly), this crops up in discussions of, shall we say, morally ambiguous topics in which the most common defense of Position X is the delightfully post-modern claim that morality is relative, situational, and individual.A little critical thought reveals that this is extremely hypocritical; on the one hand, Position X is acceptable because "what's right for you may not be what's right for me," but on the other hand only certain worldviews are allowed in discussion. Wait, what happened to relativity? Why are we suddenly refusing to respect and allow certain opinions?

Because thought experiments are fun, let's assume that religion is a lie, God does not exist, and holy books are the product of crazy/profiteering/sociopathic men thousands of years ago.

Why am I sitting here, right now, typing this? Why am I convinced, to the point of borderline depravity, of the truth of these things that are false? Why can I not willingly disbelieve in these things which are erroneous? I am governed by rationality  to a large degree, yet this one area in particular seems to have failed me. A combination of my biological composition and my environment have put me in this inescapable position. How, exactly, am I to be blamed for my condition? I am only thinking and believing in accordance with what is natural to me. For whatever indiscernible reason, I am following my genetic predisposition. Furthermore, I have no way of even knowing that my beliefs are erroneous, because no evidence seems sufficient to convince me thus. This is, as far as I can tell, an integral part of my personal identity. How then can I not use it as the basis for my stance on Position X? Must I deny my own identity in order to participate in discussion and draw conclusions?

Clearly this is absurd. The jury is still out on whether God exists, whether any religion is true, and whether holy books are divine inspiration. Hence the terms "belief" and "faith." But as long as the jury is still out (we'll find out when we die), any position drawn reasonably from faith is perfectly valid. There is no basis for excluding respectful, polite, and reasoned argument from an honest discussion. No point is automatically ignorant, hateful, bigoted, or apathetic because it stems from religious belief.Contrary to what is often claimed, anyone who uses Person B's "without using your worldview to support your claim" argument is immediately identifying oneself as the more closed-minded party in the discussion.

If you want to debate, feel free. Just don't insult my intelligence by expecting me not to argue from my worldview. That's utter nonsense.