There is a mathematical definition of consistency that I was referring to. It basically means that you can prove that a model can't be used to create a contradiction. In maths, any model where you can't prove that is disqualified for most work.

Problem is, the numbers we use don't actually satisfy that standard. There is at least a chance that it isn't possible to create a correct model at all using what we generally call "numbers". If someone were to stand up and "complete" Godel's work, so to speak, that would invalidate all of science (Godel proved it isn't possible to prove science correct, so completing his project would be to find an actual deep, unsolveable problem with numbers. A number of good candidates have crept up over the years, famously the axiom of choice debacle, and a lot of interesting paradoxes, like "does the collection that contains every collection that doesn't contain itself contain itself ?" (last 4 words - not a typo))

There's actually 3 different consistency standards for models (and number 4 is that it's not consistent at all):

1) consistent <- we can prove it !

2) inconsistent <- we don't know, but we may find out at some point in the future

3) inconsistent <- we don't know, and we can prove we don't know, that we will never know

4) inconsistent <- we have an actual counterexample, and thus a proof that it's inconsistent

Science falls in the third category. So does (Christian) religion [1]. There is no real difference in consistency between science and faith by this standard. Problem is that other standards have similar problems. Again a distinction should be made between different religions, as there's only one where I've ever seen any serious discussion on the side of the religion.

a) verifiability : faith is not verifiable. A Christian would say that's part of the point. Of course, neither are most sciences. Certain aspects of mathematics are not verifiable (the other godel theorem), either not at all, not by any finite procedure, or not by any reasonable amount of effort. For physics there is actually only a relatively small portion that is directly verifiable, and once you go down the ladder ... verifiability becomes a distant memory by the time you get to things like history.

Btw: a misconception you seem to have is that theories get modified because of inconsistencies. Well, I'm not saying it never happens, but in practice theories get modified because there's a need for it. Architecture, for example, works with pre-Newtonian physics (buildings architects calculate on stand on a disc suspended in space, with a constant gravity vector straight down, in a barely viscous liquid. Has been that way since before Newton was born, and there's no good reason to change it, so nobody did (in fact there's good reasons not to change it, complexity for one)). Yes this is the utilitarian argument, but it's true. It may not control all academic activity but it controls 99.99% or more. If anything, it's been getting worse.

An illustration of that fact can be found in physics for example. Relativity was discovered because of the black body problem. You see, Newtonian physics predict that if you heat up any object, the universe should explode. Obviously it doesn't, and this was an eyesore. Now keep in mind that Einstein was a patent office clerk with a weird hobby, and this is no coincidence : there wasn't all that much attention going to that problem. Every theory has eyesores. Currently there are 2 huge established theories, and one that everybody believes in but no convincing predictions have been made using it. Here's the current eyesores : relativity theory only has gravity, doesn't have particles or any force (gravity's not actually a force in that theory), has a continuous infinite universe that is either flat or just ever so slightly bent (like a millimeter per lightyear or so). The standard model doesn't have gravity, yet things fall, it has a discontiuous universe that is bent twisted and shifting beyond recognition at small scales, it fails to predict large scale objects in any reasonable manner (e.g. large scale universe is obviously mostly flat ... why ? How does the shifting particle soup that is the standard model's playground become the flat expanse we call space where a photon can fly undisturbed for millions of lightyears ? This, to me, is not a small detail you can just gloss over), yet we can design things like cell phone radios and cpus using it. Then there's string theory ... string theory however is a theory with so many open ends that you can do pretty much anything what you want with it. It answers the question "hows does the universe work", by giving you a brainfuck compiler and get cracking on a simulation, stating that the answer is in there (and of course, it is, in the sense that you can probably write a correct simulation in it). Those are current eyesores. I sure hope some people at the patent office are about to fix them, because I doubt significant heyway will be made any time soon.

b) predictability. I would argue that religion makes predictions, and I would argue that, averaged, they're pretty good. E.g. islam says camel piss is good for you [2]. This sounds ridiculous of course, but taking 2 facts into account it makes sense, somewhat. First urine is the one bodily liquid that is sterile. If you care about disease spreading, you can't eat or touch the same food as someone else, you can't drink the same water, you of course can't have sex or other things that exchange bodily fluids, certainly not with animals, but urine is an exception, it's fine, it's sterile, it's safe. If you don't have a water source you trust, camel piss may be preferable. Knowing that poisoning water supplies was standard Roman army practice, it may make sense if you're waging a war on them. Eventually of course, it'll kill you, but only after months of drinking it. But it's not a stupid, random piece of gibberish either. And religion certainly makes predictions about what will happen, most of which you'll find yourself in agreement with.

A lot of sciences don't care about predictability. Maths would be one example. We study models, because of their implications, and because we like the idea of, shall we say, "classifying" logic. This is a fool's errand, but it's fun. "This does not predict a thing" is a perfectly valid criticism of all but one project I'm involved in, and that's because it's beside the point.

Obviously predictive ability is one aspect of the utilitarian view of science, so it can't be ignored completely. But most physics theories that are being actually worked on (in other words : string theory and nothing else), do not have any demonstrated predictive ability that I am aware of.

And how does e.g. history fit in with predictability at all ? I would argue that religion definitely scores higher on predictive ability than the humanities, somewhat lower than most exact sciences.

c) falsifiability. Again most sciences aren't falsifiable. Mathematical models work with axioms, and falsifying correctly constructed models is impossible (with of course, the glaring exception of the natural numbers (and thus rational numbers, and real numbers, complex numbers and anything based on them), which we know may be falsifiable. This is considered very, very bad)

But string theory for example isn't falsifiable. And again, how does that work for the humanities ? Any statistical work effectively isn't falsifiable. Take climate theory for example. It hangs together from approximated differential equations. The predictions made using them by the IPCC in 1990's ... well, they were wrong. I mean I'm not saying the earth isn't warming, but the IPCC's numbers from the 1990s are bullshit, but they correctly point out that that doesn't actually falsifies their models' claims (although, frankly, it does prove their error margins calculation is ridiculous). They only claim that to a best approximation, their model is what should happen to the variables they're monitoring over time. Medicine is the same. For most medicines we have a double blind study. Now you should think, really hard, about what the exact claim is that is made by those studies and how it's verified. You'll see the truck-sized hole in the thinking.

d) ...

The greater point here is that these are all standards of correctness, trustworthiness, "truth". They're all different, they all have their uses, and they are followed in various ways by various sciences. Within individual sciences, there tends to be a whole spectrum of theories that rank differently on all of these standards. Religion is no different. It simply has a place on the spectrum, just like any science does. Various components of religion very on where they fall on all these standards.

But it is certainly not the case that sciences score higher than religion on all of these standards, it is simply the case that there is utilitarian need for both, and for criticism of both. Science has it's uses, and so does religion. Where things fall on standards of consistency, falsifiability, predictive ability, ... is simply a property of whatever fills that particular niche best.

[1] https://www.uwgb.edu/dutchs/PSEUDOSC/RammReconcile.HTM
[2] https://au.answers.yahoo.com/question/index?qid=201204210704...