And yet the most common trump card played against skeptics is that we aren't [open] minded enough and we dismiss incredible claims too quickly.
It's not a trump card, in the sense that while it may seem to signal an end or a major shift in debate, I doubt the typical reader will be fooled. It's not so much a trump card as a table-flip.
I've written at length on just how "open-minded" fringe claimants really are, so I'll just summarize here. "Open-mindedness" as used in fringe arguments typically means only open-minded enough to accept the fringe claim. It doesn't mean accepting similar fringe claims. More specifically, the fringe claimant advocating "open-mindedness" has never been so open-minded as to consider the possibility that he himself might be wrong. Hence it reduces to special pleading. Jabba has specifically been asked whether admitting failure is an option. He has not answered, so I assume he's not open-minded to the extent he'll consider his own errors.
This rhetoric always has the effect of begging one's critics to accept a lower standard of proof, and it almost always comes across that way to a dispassionate reader. It's an emotional ploy. People want to be thought of as "open-minded," so the fringe claimant just redefines what that means. In the larger sense, the contention is often between fringe claimants and skeptics and their modes of thought. As you note, skeptics are characterized as rigid, narrow thinkers (in a bad way), and fringe claimants are imaginative, free thinkers who accept a broader range of possibilities. Hence there is a desire to insinuate, "If you don't accept my claims on my terms, you're too rigid a thinker to be worthwhile."
As to premature dismissal of claims, that's just not true. Which is to say, you're right in alleging that it appears true, but even a cursory examination of the facts satisfies the accusation. A fringe claimant's fatal error often appears early on. Bubba, for example, simply does hit-and-run posts with no supporting evidence. These need no detailed rebuttals, even if the intent was to bait one.
In Jabba's case he's literally had four years to make his case. The extreme indulgence expended in trying to engage him cannot possibly be construed as a premature rejection.
...he hasn't done us the base courtesy of even acted like he's listened to anything we said.
This is very true. It's a sort of high-functioning rudeness. It's not the kind of personal sparring that gets moderated away. It's the Dolores Umbridge sort of approach where one is not immediately objectionable, but the overall calculated effect is quite discernibly distasteful.
