The methods of science may well be theologically neutral. An experiment runs and is either destined to accept or reject the null hypothesis. As these experiments build up and explanations build up along side them, we start to build a body of knowledge. That body of knowledge is not theologically neutral. It has theological implications.
If we take the one of the most basic theological ideas–that nature is managed by a personal being–we can justify certain expectations. One of those expectations is that the running of nature would alter or waver to fulfil the preference or judgement of the managing God: we might expect to see the sun stand still in the sky to extend a deadline, or gravity be reversed to physically lift a person from an uncomfortable situation. And, in pre-scientific times that is exactly the narrative people built. The Old Testament is filled with such miracles. Science has discovered that nature does not show exception in its running.
Tsunamis are not held back by an invisible wall and crops do not grow regardless of the physical environment. This “pitiless indifferent” nature has important theological consequences. Religions have adapted and folded and felled cornerstone beliefs to accommodate science simply because science has such a profound theological input.
As your theology gets more specific–say, Literal Christianity–science is yet more profound with its theological input. The evidence does not support the Genesis account of the origins of the universe (Young or Old Earth). Many people claim that religion has adapted and those literal interpretations are a childish place for an atheist to direct its criticisms. But the fact that religions have adapted to yielded to science only goes to show the theological input that science has had.