Very serious Christians (e.g. those who deny science on the grounds that it contradicts the Bible) and very serious atheists (e.g. those who deny religion on the grounds that religious books contradict science) both tend toward the high end of the Buxton Index. The people who ignore the contradiction and are only religious on Sundays tend toward the low end.
I don't think this is as symmetric. Denying religion on the grounds of contradictions with logic and science is an extremely common position between atheists, probably damn close to universal in the west. Denying science altogether (prayer instead of medicine, flat earth, etc.) is fringe, even amongst fundamentalists. That said, I have always said I respect fundamentalists more because at least they take their ideals seriously. So, yes, you might be right. Those that refuse science have resolved the contradiction the other way around, but ultimately may be suffering of the same 'condition'.
The terms Near and Far are to be taken in the context of Robin Hanson's Near/Far articles.
I was reading a fairly convincing article linked from a comment here about how theistic beliefs are so scantly supported, when not outright contradictory, that it's a doubtful whether anyone truly holds them at all. Of course there is a whole battery of explanations around the self-deception, signalling and belief-in-belief cluster, but the question that got in my head was about the kinds of people that can or cannot profess to hold these beliefs.
A common thread in many a 'deconversion' story is that some inconsistency in a person's worldview comes to their attention, and they can't let go until they have undone the whole fabric of their belief system. But given that most people are happy living productive lives while simultaneously nominally carrying around massively conflicted worldviews, what is it that makes certain individuals not capable of this fairly common human feat?
So the hypothesis that I'm considering is that the people who came to atheism this way, are those who demand detailed consistency of their Far ideals. Alternatively, they could be those for who what is normally considered Far is actually Near, in other words those with an unusually high Buxton Index. Combining the two, perhaps for people with a high Buxton Index, Far simply evaporates, as it comes under the scope of things that are relevant to a person's planning. (Edsger W. Djikstra, when introducing the Buxton Index, says that "true christians" have a Buxton Index of infinity. I think that couldn't be more wrong. Perhaps it is the case for singularitarians though.)
The obvious reason to be suspicious of this idea is that it's very flattering for those that fall in this category, which includes myself. Rather than dithering about it, I'd rather expose it to the community and see if it seems to have legs in the eyes of others.