Most religious statements set themselves up to be unfalsifiable, and that's really the main trick behind most of these ideas, but to work they have to make certain claims about the nature of the universe that are exceedingly unlikely, or in other words: just completely made up.

The kind of evidence we gather through scientific observation points to a world that works completely without supernatural intervention, and with advancing scientific knowledge the kind of acrobatics you have to perform just in order to keep escaping the light radius of discovery become more and more elaborate, outright denial of evidence becomes necessary.

For example, to claim that the Earth is 6000 years old, you have to discard a lot of paleontological evidence. To deny evolution, or any other established scientific model, you pretty much have to make the conscious decision to ignore data. The way this works is usually by some invocation of all-powerfulness: my deity is all-powerful, so due to that it not only faked all the evidence, it also made itself invisible and undetectable.

I agree though that it's not possible to disprove arbitrary fantasies on their own terms. All we can do is measure and model things within reasonable limits. Far, far outside these reasonable limits, everything is theoretically possible, it's just not compatible with reality in any meaningful way.

From the perspective of a person on the outside looking into this religiously contaminated world, the most upsetting and depressing thing is that people know their beliefs are completely made up on a whim, and in full knowledge of how that process works, they still believe all this crap without an ounce of skepticism.