Alright. In attempting to clarify what I may have perceived or misperceived about the ways in which your views may coalesce with my own, I think I see now that this is both some similarity and some difference. On the side of similarity, we can both affirm that religion, like most human cognitions, express some kind of human mental constructs also predicated upon human wants, needs, desires, etc. With that, we're similar on a very general scale, so far so good.
However, more in line with some of the things
@Silmarien said above, I'm going to have to say that the term "natural," as you are attempting to use it, is slightly bigger and may contain too many distinctions that those like me could make in denoting Subjectivity from Objectivity, and from full Artificiality from realistically drawn and conceived essences within our (shared?) Reality. This would mean that there may also be a continuum on which the disposition and acting out of "irreligiousity" becomes something that isn't necessarily "natural."

I fear I have to disagree with almost everything here. Sorry.
Perhaps I am wrong or unjustified, but I would make the distinction between "natural" and "artificial" on quite the opposite side of what you seem to suggest. If I got you right... I'm not quite sure about that.
"Natural", in my view, is just the way things work. In that case, it is the way the human brain works.
I'd say you are aware of that: our brain, the subconscious as well as the conscious parts, but especially the subconscious, work sometimes (often? always?) quite differently from what we "want, need, desire". It takes direct and persistent conscious effort to shift these ways... but even then, the ability of the brain to retrain itself, at least partially, is "natural"... the way it works.
The wants, needs and desires... these are what drive the "artificial" part. This is how we take "what is" (natural) and try to turn it into "what ought to be" (artificial).
As I see it, both the search for patterns, the search for agenda, the search for a narrative and the search for answers... these are all part of this "natural" way our brain works. It is what makes us humans. And it is what drives both religiosity and irreligiosity. It is just a question of how far the quest goes and what path it takes.
But the pattern that we "identify" (or, make up), the agenda, the story, the specific answers... these are based on the "artificial" parts.
So the "disposition" is
always natural. There is no fundamental difference between the "religious" and the "irreligious" side... they both employ the same mechanisms. But the "acting out" is always "artificial"... and both the involved mechanisms as well as the results can differ widely.
Sometimes, it may be; sometimes it might instead be an abnormal expression depending on exactly what relative angle of viewing we look at it. I guess in this regard, we could take Judas as an example of unnatural religion---the guy should have know, but just couldn't find it in himself to follow through; although Saul (before he became Paul) could be seen as a kind of more "natural" irreligious response. Thank God Jesus knocked him on his natural keester before he could do any real damage to Christianity .............. !
Hm again.
I don't know what I would make of the Judas character. In some (non canonical) stories, he's the hero, doing what needs to be done, even if it means his downfall. His role in the canonical gospels is... vague.
The problem that I have with most of these characters is that I cannot see them as real people... the whole set of the disciples seems, for the most part, more of a staffage than characters. Something for Jesus to act upon. Props. So it's quite difficult to do a character analysis on them.
Personally, I would place Judas in the "irreligious" side: the one who believed, and was disapointed to the point of disbelief. He became the betrayer because he felt betrayed. His chosen deity had turned out to disappoint him.
In a similar way, I would put Paul/Saul on the "religious" side. If the narrative is to be trusted, he was personally interested in the persecution of this new Christian group... and there is simply no "irreligious" motive for that. On that other hand, the defense of an existing religious belief against a potentially dangerous enemy is a strong religious motive, even a natural one. Even using my definition.