Atheist VS Naturalist - the latter sounds more appealing to me...

[Belacqua]

up until this point, every cause for a physical phenomenon we’ve ever explained has been a natural one

I think I addressed this before.

The scientific method is set up to find natural causes. It's no surprise that every cause it has found has been natural. It finds what it's set up to find.

As poly says, if there is no natural explanation, science just assumes that there will be one later. That may be true or not. 

what reason is there to think that the supernatural is even a possibility as the cause of anything in the first place?

I don't know if we have reasons or not at this point. 

I'm only saying that our methods are very limited and we shouldn't beg the question.

At least in the case of philosophical naturalism, we have enough examples that we can make an inference.

We can infer that if science finds an explanation, it will be a natural one. If we assume from this that nothing supernatural happens, we are begging the question. If we assume from this that there is nothing in the world science can't address, we are begging the question. Science finds natural explanation because that's what it can look for.

I agree with you that we should look at past discoveries to guide us. Given the age of the universe, the history of people trying to explain the world (the natural world or not) is pretty short. History teaches us that people present systems that seem good to them, and have trouble imagining different systems. Then another system comes along. Each system has a genealogy, limitations, and a particular contingent point of view. When I said earlier today that our minds aren't intrinsically tied into the mind of God, that's what I meant. 

Our current system seems like the best ever. Maybe it is. Experience teaches us that it will probably get replaced. 

The scientific method demands repeatable empirical evidence to reach tentative conclusions. It attempts to find "the view from nowhere" -- that is, a view that's not contingency on human limitations or presumptions. I am skeptical that such a view is possible. All views are "views from somewhere," based on where we are and what we're able to take in.

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It’s not the unbeliever’s responsibility to consider it, without good reason, as a possible cause in every instance, or assume it is the cause when he can’t find a natural answer.

I'm not asking anyone to consider it without good reason. Science can't consider it, because science only considers the natural.

I'm saying that assuming its non-existence, a priori, is begging the question. But I'm sure you can have a long happy life and solve many science problems without ever once thinking about the supernatural.

Also keep in mind that, since Newton, science advances by agreeing not to answer certain questions. Science doesn't necessarily say why things happen. It describes and quantifies what happens. But just as Newton decided to describe and quantify gravity without having the faintest idea what gravity is, modern science also gives the answers it can give and remains quiet on those it can't. 

If you don't want to think about the questions science can't address, that's fine. That's your taste.