A similar situation that used to happen frequently to me in real life, was when the argument was too long, too complex, used information that I couldn't verify... or ever could, but the verification would take a lot of time... something like: "There is this 1000 pages long book containing complex philosophical arguments and information from non-mainstream but cited sources, which totally proves that my religion is correct." And there is nothing obviously incorrect within the first five pages. But I am certainly not going to read it all. And the other person tries to use my self-image of an intelligent person against me, insisting that I should promise that I will read the whole book and then debate about it (which is supposedly the rational thing to do in such situation: hey, here is the evidence, you just refuse to look at it), or else I am not really intelligent.

And in such situations I just waved my hands and said -- well, I guess you just have to consider me unintelligent -- and went away.

I didn't think about how to formalize this properly. It was just this: I recognize the trap, and refuse to walk inside. If it happened to me these days, I could probably try explaining my reaction in Bayesian terms, but it would be still socially awkward. I mean, in the case of religion, the true answer would show that I believe my opponent is either dishonest or stupid (which is why I expect him to give me false arguments); which is not a nice thing to say to people. And yeah, it seems similar to ignoring evidence for irrational reasons.