A skeptical observer cannot accept extraordinary claims based only upon anecdotal evidence. Humans are subject to cognitive bias and are therefore unreliable; the skeptic must weigh the probability of the claim being true vs the probably that the claimant has fallen victim to cognitive bias.
Of course, this doesn't apply to inconsequential claims. If someone tells the skeptic that they went to the movies with a friend, the skeptic need not demand corroborating evidence in order to accept the story as true, because if it turns out to be false then it is entirely unimportant. However, most claims about gods and the supernatural are not inconsequential. Religion is often used as a tool to control people, by prescribing morality and making threats of eternal punishment, and superstition is used as a means to swindle people by exploiting their beliefs to sell fraudulent products and services.
But while it's relatively easy to question the reliability of another person's testimony, it is considerably more difficult to apply the same critical standard to the things that oneself has witnessed. A recurring theme in the stories of people who believe in gods, ghosts, alien visitors etc. is a powerful personal experience of some kind. Their own personal vision on the road to Damascus. Their personal experiences are powerful because it is difficult to write off one's own memories and sensory experiences as cognitive errors.
This is why a person can be simultaneously skeptical of ghosts and alien visitors while simultaneously believing in the existence of Yahweh on the basis of a personal experience. Without that personal experience, they may well be skeptical of Yahweh, too.
The believer may recognise why other people are skeptical of their belief: they may recognise that other people do not have the opportunity to see the evidence for themselves. But this becomes a built-in defence mechanism: the believer's convictions become unassailable because no matter what skeptic says, the believer can always reassure themselves that the skeptics would be believers too if they had the same experiences.
TL;DR: Powerful personal experiences cause people to steadfastly believe extraordinary things while lacking the means to present convincing evidence to a open-minded yet critical audience.
Of course, this doesn't apply to inconsequential claims. If someone tells the skeptic that they went to the movies with a friend, the skeptic need not demand corroborating evidence in order to accept the story as true, because if it turns out to be false then it is entirely unimportant. However, most claims about gods and the supernatural are not inconsequential. Religion is often used as a tool to control people, by prescribing morality and making threats of eternal punishment, and superstition is used as a means to swindle people by exploiting their beliefs to sell fraudulent products and services.
But while it's relatively easy to question the reliability of another person's testimony, it is considerably more difficult to apply the same critical standard to the things that oneself has witnessed. A recurring theme in the stories of people who believe in gods, ghosts, alien visitors etc. is a powerful personal experience of some kind. Their own personal vision on the road to Damascus. Their personal experiences are powerful because it is difficult to write off one's own memories and sensory experiences as cognitive errors.
This is why a person can be simultaneously skeptical of ghosts and alien visitors while simultaneously believing in the existence of Yahweh on the basis of a personal experience. Without that personal experience, they may well be skeptical of Yahweh, too.
The believer may recognise why other people are skeptical of their belief: they may recognise that other people do not have the opportunity to see the evidence for themselves. But this becomes a built-in defence mechanism: the believer's convictions become unassailable because no matter what skeptic says, the believer can always reassure themselves that the skeptics would be believers too if they had the same experiences.
TL;DR: Powerful personal experiences cause people to steadfastly believe extraordinary things while lacking the means to present convincing evidence to a open-minded yet critical audience.