I think a just as important question is: “What would it take for those who believe in things such as ESP, alien visitation, etc. to admit that they may be wrong and that such things don’t exist?” When phrased that way, they will start moving the goal posts, resort to special pleading and all sorts of mental gymnastics and logical fallacies in order to maintain their belief. Their minds are the ones truly closed. They are never open to the possibility that they might be wrong.
I think the biggest part of the problem is that they watch too much fantasy on television and have trouble remembering that it’s fiction. You can trace the “close-minded skeptic” back to the original Night Stalker television series. Carl Kolchak was not the kind of person to believe in the supernatural without hard evidence, but in the series he kept stumbling over this evidence every time he turned around. This caused a problem for the writers, namely his editors, police and other authority figures. If they believed him, it would make his job too easy and the episode would be over too quick. So the authority figures all had to be skeptics. Which made sense the first episode or two, but you see the problem. Every episode had more and more supernatural stuff, so the authority figures had to get more and more ridiculously, stubbornly, pathologically close-minded. It was required for the premise. By now, every fictional movie about the supernatural assumes the “pathologically close-minded skeptic” myth.