No, ceo, science is hostile to supernatural causes because every newly found material cause pushes back the god of the gaps. It is not faries that make things fall, but gravity. It is not sprites that create lightning. It is foolish to say that science is indifferent to supernatural causes. While it is true that maintstream science does not seek to disprove them, as that is impossible, science flatly contradicts a huge number of supernatural causes. You cannot show that the ressurection of Lazarus occured, and you cannot show it had a supernatual cause. When science contradicts the supernatural, we reject it. Supernatural explananations have never lead to further discoveries about the world, which is the very essence of science.
Science deals in material efficient causes. But science asserts what it can demonstrate, and it does not assert that no other kind of causation exists (say, final causes or non-material efficient causes). Why not?
That's a metaphysical proposition, not an empirical one. You're confusing philosophical materialism (or scientism, if you like) with science, and assuming that the philosophical-materialist response is necessarily the scientific one. I can't help thinking that a little more background in both philosophical and scientific method would have delivered you from this error.
As I've previously pointed out, despite its extraordinary usefulness, the limitations of the scientific method are rather obvious. This is true even where science has already proposed a complete, workable physical explanation. Even in such a case, science cannot - and does not presume to - tell us whether we have arrived at the
only complete explanation, or indeed even the simplest or best possible
scientific explanation. It can only tell us when we
haven't found such an explanation (by proceeding to find a better or simpler one).
As for your reference to the "god of the gaps", it can fairly be said that the deity posited by traditional Christianity isn't a god of the gaps in the first place. I might describe the god posited by
some Christians as one, but by and large the god of the gaps is a straw god.