Disbelief is not a claim. The particular argument that is pissing me off at the moment is the claim that atheism is a religious belief. This is absurd. Atheism is a religious belief in the same way bald is a hair color and hot water is a variety of tea.
Skepticism is the default position. The burden of proof is on the claimant. UFO abductees, astral projectors, snake oil salesmen and cult leaders all have the same responsibility to provide evidence for their claims as climate change scientists, biologists, quantum theorists and economists. (Well, maybe not the economists.)
Extraordinary claims with little or no proof should be treated as specious and/or unlikely. Telling someone that they have a ‘supernatural’ belief because they don’t accept your near death experience or a ‘religious’ belief because they don’t think Allah exists is to twist the meaning of the words beyond the breaking point. Not believing in invisible pink unicorns doesn’t mean you are a pink unicornian with a profoundly negative viewpoint.
Why does it matter? The danger in defining non-belief as a simply one viewpoint in that area is that the various believers in any foolish nonsense then feel justified in demanding equal stature and treatment with not only the default viewpoint, but any well proven scientific theory. The teaching of the baseless ideas of creationists in schools alongside Darwinian evolution is just one example of the damage this kind of thinking can do.