PoR is not a bad subset of philosophy to me, but I think I can explain why it's (at least one of) the part with the most quarrel.
1. Any philosophical thinker thinks about Region at some point and has a satisfying answer for his/herself, it's not like Hegel or Heidegger, etc, which are read and understood and discussed by a part of thinkers, and the most of the readers would not claim that they totally understand it.
2. Thinkers on Heger or Heidegger, etc, share a lot of common sense, and based on that they might agree or disagree with each other. While the thinkers on Religion are sorted into clearly 3 classes: theist, atheist, agnostic, and all disagree with each other. They do share the same world, but their ways to read the world are very different, and, as far as I observe, most people do not want to understand others' perspectives. It's certainly very hard and empirically most people don't or do with little effort.
3. Other subsets of philosophy are external knowledge that might not really affect your daily behavior, while religion is the most fundamental part of your worldview. People really defend their own fundamental beliefs.

I thought of a better way to post our difference. See whether it makes sense.

I understand your position as that the human reason is intrinsically against mysteries or supernatural, otherwise, how can it work without assuming it works, right?

I agree with this and I think it's the foundation of modern philosophy and science.

However, besides this, I also hold another more postmodern idea that reason might have its limitation, although I can not think of, with reason, a case where reason does not work, it's kind of paradoxical, I can see the possibility by analogy, however. So I suppose to save the possibility of the human reason not working in my deduction. In our case, I would accept the possible existence of influential but unexplainable things, which is against the nature of reason (I don't think so, but I understand your agreement with so).

My position brings a bunch of other issues, for instance, if the human reason is not trustable, what's the point to make a deduction at all?

But perhaps if we extinguish the light, we become aware of a vast space which is dimly lit - we can't see it in the same kind of detail, but we can sense its vastness. And that there is a kind of light inside the dark. — Wayfarer

This is a good metaphor. But in his position, the answer would be: when one holds a lamp, he can't assume there is a thing within the light range but not seen.

I agree with you. Besides, these two respectively define “the dark" different ways, and when you call "the dark" as "the dark", you have already presumptively taken some perspective.

Because any influence would give somewhere to start an explanation. — Pfhorrest

I think I fully understand your position now. There's a jumping in either my reason or yours or both, I was keeping saying "A is possible" while you kept claiming "A does not exist". Since we are both so confident, I don't think a further discussion will help, let's stop here.

Thanks for your attention.

It's kind of a loop, a god that is influential and unexplainable is denied by your categories.

We can never know if something is unexplainable, only that it is not explained yet. — Pfhorrest

I agree, but we need to leave a space for "unexplainable" in our deduction, even when we are trying to explain everything, therefore your 4 definitions of "god" can not cover all possibilities.

A god (or anything) that is influential is definitionally not supernatural on my account. — Pfhorrest

Does it mean you put the influential but unexplainable (if exists) god in the class of "incarnate", I don't get the precise definition of "incarnate", but if you use "alien" as an example, seems to me it's not a good analogy for that god I describe?

The supernaturalist posits that there is something out there that is objectively real (so far so good), but beyond our ability to investigate. — Pfhorrest

I'm not sure whether this is against your position, because "there is a thing beyond our ability to investigate" does not mean "this thing is beyond our ability to investigate".

So any opinion we hold on it must just be taken at someone’s word — maybe just our own — without question, which is exactly that kind of arrogance that “THIS is the winning play” that my principle of criticism is against. — Pfhorrest

I can‘t see how the last sentence deduces this one.

We must always proceed on the assumption that there is some answer or another out there, but that any particular proposal might not turn out to be it, if we want to have any hope of narrowing in on whatever the right answer is, if that should turn out to be possible. — Pfhorrest

I agree. But when we are talking about "supernatural" god, we are not talking about a god supernaturalists refer to, we are talking about an objective supernatural god that either exists or not. So no matter how "supernaturalists" behave (as your description or not), we should not take their behavior or their definition in our account, right? And the possibility that the supernatural god is influential but unexplainable seems to me is not neglectable, which hinders your deduction on the supernatural god.

I see your point, but I think one (like me) could assume a thing is explainable and act as so while keeping in mind the possibility of the opposite. Figuratively, a football player plays as if he will win, but he could also be aware of the possibility to lose.

“Anything might or might not be explainable” — Pfhorrest

I'm not sure what you mean by this, do you mean ("everything is explainable" or "everything is not explainable") is the least assumption, or "anything is either explainable or unexplainable" is the least assumption, or otherwise?

and that things we haven’t explained yet just haven’t been explained YET, not that they can never be explained. — Pfhorrest

I completely agree with you that we should try our best to understand or explain all phenomenon we see, I think the opposite is what you called "non-cognitivist". But I think "there might be something that is unexplainable" is a more gentle presumption than "anything is explainable". Because the fact that the world is explainable itself is not explainable ( or at least not explained), as Einstein said similarly. I suppose the burden of proof is on the "anything is explainable" side.

Hi Pfhorrest, thanks for starting these discussions. I can't go through all discussions you took, so please forgive me if I repeat other's questions.

In your "supernatural" definition of god, (I see someone made a similar argument, but I would make it more specific,) how do you consider a case that the consequence of god's activity can be observed but it does not appear in regular as a natural phenomenon like wind, therefore some people do observe the evidence of god, but can not record it so mankind can not have an agreement on god's existence.

I think there is a presumption of your classification of god: that you know the definition of "nature". However the human definition of "nation" is evolving, thousands of years ago, humankind considered lots of things as mysteries, "supernatural", "nature" is underestimated by them, and now you believe everything you experience is natural, in the faith that science will eventually explain everything. Is this belief well-founded?

I'm not sure that entropy works backward anything.

Because entropy is to measure the unknown of a system from the perspective of the observer, it's not an existing thing that makes real effects like gravity field. Image God looking at a classical gas equilibrium system, does he see entropy? No, he only sees the dynamics of all particles, all determined.

Entropy is a powerful tool for humans to modeling the phenomenological world. This is why the concept of entropy is so popular, but I think we need to keep in mind that entropy plays a role in the modeled world, not the real world. Therefore I think the effectivity of entropy is an epistemology question rather than an ontological question.