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No it isn't, because you can't prove that something doesn't exist. However, everything which has been shown to exist (is detectable by scientific experimentation) is part of the physical world.
If you are talking about things which aren't detectable, then science wouldn't be concerned with those things because they aren't worth thinking about
This is kind of wrong, and is a common conflation with respect to science. First, scientists do talk about things that cant be proven, string theory being just one of them. It's an idea of the physical world that cant be proven. If we have a way to actually test a hypothesis of string theory, it will get more attention. But if you don't have people thinking about these things, we won't have better models for describing the universe, such as relativity. Similarly, science can't prove a negative. Science will never tell you God doesn't exist or can't exist, only that we have no proof that God exists and that we have no model where he could. But our knowledge has been less complete before, and our models have been updated as knowledge is gained.
And much of philosophy has no basis in the physical world, but this doesn't mean it isn't worth thinking about.
Ok so firstly, no theory can be proven. You're thinking of theorems. One of the tests of a scientific theory is its falsifiability. A simple example would be that if a single apple floats upwards from the tree instead of falling to earth, that would falsify the theory of gravity. In string theory, the falsifiability lies in the predictions of quantum mechanics. A falsification of QM would collapse string theory immediately. Of course, you've chosen this particular theory because it is at the fringes of current understanding and there is debate over whether it's a legitimate theory. However, it is actually founded on rigorous study, and its predictions are exactly as consequential as its falsifiability is agreed upon.
While it cannot be proven using current methodologies, that problem puts it in such distinguished company as general relativity and even Galilean relativity were in terms of the experimental technology available to natural philosophers at the times of conception. String theory can be proved, or disproved, just not yet. So we don't write it off as academic, but we file it under "pending", until such a time as we are able to test it. This is absolutely the astute thing to do.
If you have a test for God, please propose it. It seems that this particular question is beyond both practical and philosophical technology at this point in human history. There is no theory about God that can be tested, falsified, repeated and scrutinised as far as I know, so why would science waste time on this question? Maybe in the future we will have a knife of some kind that can carve meaning into this question, but we don't at the moment. There's a separate discipline for pondering abstract questions which we can't test, it's called philosophy. And it pushes science, when the time is right, to find evidence. But until philosophers find a way to test their suppositions, their suppositions are not worth thinking about,for a scientist.
That's precisely why I chose string theory, because it does have value, even if it can't be tested at this time. Yet, even though little can be done to advance it, shrugging and ignoring it won't change that state, if you're a scientist.
As for the pondering of philosophers, there is a good chance that many of their questions will never be answered, and yes, there would be little value to study them, as a scientist. But that qualifier has a dramatic effect on your previous statements.