In your opinion.
Of course, those of us to believe that the spiritual world is no less natural, the term 'scientific' has to be included as a distinguishing adjective.
Well, the obvious methodology is a spiritual one which doesn't fit with a merely scientific outlook, so that those who don't believe in the former won't understand it anyway - which is why I've regularly stated that the debate is somewhat moot as the different protaganists are starting from very different definitions, positions and understandings.
Science will never be able to prove that the spiritual element of nature doesn't/can't exist nor will it's proponents ever be in a position to even cast doubt on it. I realise that you and others have tried hard to do so, but every time one or other of you comes up with another 'appeal to science' you simply point to the fact that you don't understand the other part of the natural world.
I assume, of course, that you accept that there is such a thing as the 'natural world.' Your last sentence seems to suggest that you do, indeed, think that this is so.
So, now, let's take your 'spiritual element of nature', which is the view that at least some phenomena are the result of forces emanating from this spiritual element. Any methodology verifying this would not only have to show that certain phenomena are explained only by spiritual means, but would have to eliminate the possibility of any natural explanations. Further, such a process, to have reasonable integrity, should have a falsifiability factor built in. Unfortunately, there doesn't seem to be any sort of methodology of this sort which can verify this 'spiritual element'.
However, contrary to your view, methodological naturalism could actually go a long way in confirming this by showing that at least one one phenomenon cannot be naturally explicable. In this sense, your 'spiritual element' needs methodological naturalism to demonstrate its viability.
I would have assumed that there is plenty of empirical evidence to support the idea that there is indeed a natural world, of which we are a part. I don't dismiss the idea that a spiritual world also exists, just that I see no evidence for it, until, of course, you are willing to present evidence which is in compliance with the above definition for its methodology.
To state that "you don't understand the other part of the natural world" does not necessarily follow. It could well be a case of simply not having the evidence in making such a claim leads one to dismiss the idea of a 'spiritual element' as not probable, that is until that evidence arrives. You see, it is not necessarily a case of not understanding, but simply not agreeing.