Pick any two of those aforementioned groups, and you'll find plenty of members from one who consider the other's members to have unfathomably bad reasoning and common-sense skills. And yet, somehow, some members of all those groups bear wonderful intellectual fruit.
Or another way to look at it, we could reduce almost all questions, in science or religion, to something like "what is the nature of this stuff around me?"
A subpart, "how can I interact with the stuff?" A subpart of that question, in turn, is "what are the consequences of those interactions?"
Sometimes the stuff around you is carbon. You can burn it or build things with it. If you breathe enough of it in certain forms, you might suffocate.
Sometimes the stuff around you is other people. You can help them or hurt them in a near endless variety of ways. The consequences are complex but it's generally better to not be a dick, for a variety of reasons.
Maybe the stuff around you is... all of reality? Which may or may not be controlled by a unimaginably powerful law giver. Maybe not, but if so, that would certainly affect the consequences of a lot of actions, so it would be worth trying to work out how that system worked if that was the deal.
To be clear, I'm not arguing for Pascal's wager here, I'm just needling the idea of non overlapping magisteria.
Isn't it all just, "How does reality work?"
My immediate thought was that if you assume the 'teaching domains' of science and religion do not overlap at all, then the domain of religion is vanishingly small.
If you accept that science covers (at least) all observable things, and also hold the idea of NOMA, then religion must never deal with anything observable. The teaching domain of the unobservable seems like it would be near non-existent.
Alternately, let's start from the position that a supernatural power exists and cares about what we do. Why would we be interested in that? We would be interested if that supernatural power has the ability to affect our lives/the world we live in, or will affect our lives after we die/some other aspect of some supernatural world beyond this one.
If the power can affect this world, we should be able to observe that interaction. If it is literally impossible to measure any effect, it is the same as if the power is not interacting with the world at all. Which is to say, if the power interacts with the world, then those interactions fall under the domain of science.
If the power does not interact with the world, then we can only be interested in what effect our actions, choices, and beliefs will have outside this world, on the supernatural or afterlife. The thing is, we have no way of knowing what that would be, because communicating any of that information to us would count as interacting with the world.
Thus, anyone claiming that something should or shouldn't be believed or done, for religious reasons, is either making a testable claim or claiming something which has no reason to be believed.
If the magesteria of science and religion truly are non overlapping, it seems that religion's must necessarily be very very small.
I haven't been a Muslim or a Buddhist, but I was a Mormon missionary who taught Buddhists of many sects, plus South American Catholics, European atheists, Muslims, Raelians, and your odd Yakuza while I lived in Japan.
I was taught to respect these people for what they had already learned and experienced, and to teach them a simple, elegant model of my belief system. In studying that model I realized that I hold and have the responsibility to shape, apply, and evaluate multiple models of my religion through my own life experience. This becomes an ever-evolving science that is in principle one and the same with the more technological science posted here. There are deeper qualitative questions and experiential aspects and anecdotes that are really more like fractals than questions, open to broad and deep exploration. But those elegant models, the simple ones--right in there you have a huge amount of religious people who really don't differ much from your complete-opposite anecdotal scientist in the important ways.
I could go right now and google reasons why Mormons and science don't mix, or I could go out and find a Mormon who would argue with most any scientist (come to think of it, my Mom is a good one!), but the boundaries there are in the end just different from my own and I find there's absolutely room for that. I hold my own models lightly, and compare them with others' from time to time. But--and I doubt I'm some freak religious exception here--nobody is dictating my models and their composition / combination to me. I act in many ways in respect to my church like a robot (Sunday? Church!), not because I have to, but because in my mind, the overall experiment is yielding good results and I'll change variables as I need to when I examine them. I got the feeling that others in other religions act and feel basically the same way. As I mold my models I think of myself as a type of scientist, and hope any scientist would consider the study of religion from a scientific view (model all the time, measure what you can) as an absolute (and hopefully enjoyable) mandate.
The wonderful intellectual fruit you speak of is something I experienced first hand when I was a BYU student. As a teenager I was told how wrong evolution was by my dad (an extremely educated man himself with multiple degrees), heard how certain it was from my sunday school teacher (a respected surgeon), and then I went off to my BYU biology class and was immediately taught about talk.origins and told "hey if you guys (freshmen) don't believe in evolution that's fine, but at least educate yourself". This was a huge faith-strengthener to me; a diversity of models is not only OK but developing one's own educated models was seen as wisdom in a nutshell.
I'm not sure how you'd get that from my original comment. But rereading it today, I realize I wasn't very clear. I apologise for that. Let me restate it more explicitly:
1. To be done well, science and engineering require careful thought and, to a certain extent, sound reasoning.
2. Some people holding world view "A" consider the holding of world view "B" to be intellectually indefensible, for many values of "A" and "B".
3. And yet we have plenty of empirical evidence that good science and engineering work is being done across all of those world-view-holding groups.
As far as why this particular article made me thing of this issue, it's because Mormons are sometimes ridiculed in (at least) U.S. popular culture for holding an intellectually indefensible world view. E.g., [0].