So I could ask them, "Why should I believe an account of a random person with a spooky story that makes no sense?" and immediately I am being even more closed-minded even though I was asking a question that they can't honestly answer with facts.
To them I would say that it is not a virtue to be easily persuaded. Critical thinking is the key. Critical thinking actually requires an open mind, and simply requiring evidence before believing something is no more 'closed-minded' than to claim that faith is a virtue.
On top of that, personal anecdotes about the unexplained are not evidence of the existence of any god, especially yours, and cannot be explained by God any better than they are explained by the magical actions of the mythical tooth fairy.
So we have to ask who shows the most willingness to consider new ideas. Is it the faithful or the skeptical?