It's impossible to expect that we might be philosophers all of the time, thoroughly analyzing the logical and natural foundations of every individual belief we hold. However, it is of paramount importance that we do our best to examine why we believe the things we believe.
Regarding the impossibility of disproving the existence of supernatural beings, the simple fact that it may be impossible to categorically disprove the claim that supernatural beings exist does not make the claim viable, acceptable, or (need I say it) true. "The fact that a question can be phrased in a grammatically correct ... sentence doesn't make it meaningful, or entitle it to our serious attention." Any one of us has the ability to contrive an endless stream of undisprovable claims; "there are fairies in my garden and they disappear when anyone else looks"; "I was abducted by aliens, and they removed all traces of evidence regarding the abduction"; "we live in the Matrix and I am the Architect, but I have no inclination to prove it."
In the matter of humans being unable to disprove the claim that supernatural beings exist; "the burden of proof rests with the believers, not the non-believers ... None of us feels an obligation to disprove any of the millions of far-fetched things that a fertile or facetious imagination might dream up ... That you cannot prove [the] non-existence [of the supernatural] is accepted and trivial, if only in the sense that we can never absolutely prove the non-existence of anything. What matters is not whether [the existence of supernatural beings] is disprovable ([it] isn't) but whether [their] existence is probable." The idea that humans can, should be able to, or might in the future be able to prove and disprove any and every claim is a misunderstanding of the human capacity for reason, and an overestimation of our ability to interact with the world around us. Humans have limitations, and it is the recognition and acceptance of these limitations that permits reason in the first place.
The point is that the inability to experience the object of an idea does not confer validity on the idea. How could it? Why do we believe the things we believe? Is it because of evidence, or lack thereof? Why do we believe that the sun will rise tomorrow? Why do we believe that we should be nice to people? Experience. It is experience that confers validity on our claims and beliefs. It is experience, not inexperience, that causes us to form and update our beliefs and theories, whether we make these updates consciously or subconsciously.
One of the most interesting aspects of this particular debate is that it's not endless, as many a nihilist may wax philosophical about. Disprovability does not confer validity. (Done.)