It is a cliche statement to hear that science and religion are pitted against one another. There are many Theist and Deist arguments against such a statement as they assert that science and religion coexist and that science can be used to prove the existence of God. This is a mistaken approach as science and religion do not deal with claims of the same type. There is good reason to be skeptical of any proof or refutation of God reliant on empirical claims.
To begin with, science deals with the realm of empirical claims. These are statements about the physical universe and are claims that we must be able to accept or deny based on observation. We do this by formulating a hypothesis, and then creating experiments designed to test the aforementioned hypotheses. If we find conclusive evidence to infer that a certain hypothesis is true, then we accept it. This all sounds good, so why do I object to the usage of scientific methods in religion?
Science is concerned with the testing of empirical claims. It has nothing to do with proving or denying non-empirical claims. Science cannot be used to prove or disprove the existence of God or of various other metaphysical claims. I once had to design an experiment for souls as part of a group project in school, and the best we thought of was to weigh a body right after death to see if any change had occurred. This was total nonsense because souls, if they exist, are incorporeal entities and thus would not have caused a change in weight if they departed the body.
I expect some to object and say that we ought not to deal with "unscientific claims" but this doesn't really make them go away. Suppose for a moment that souls exist. We would still be unable to ascertain information about them through the scientific method. The knowledge we could gain about them doesn't change regardless of their actual true or false values. The same is true for other metaphysical claims such as God, free will or minds. Some of these can be proved through logic while others are unknowable. It is incumbent upon us to use appropriate epistemological methods when dealing with various claims.
Science may occasionally be used to refute certain Theist arguments, but this is more limited in scope than many realize. There is no merit in trying to debunk Jesus walking on water by trying to demonstrate the impossibility of the task by analysis of the components of water. The claim is a supernatural one, and not a natural one. Therefore, the events of the claim are not homogenous and not equivalent. This isn't to say that one should accept the claim on face value, but only to realize that we ought to be careful with what proofs and refutations are composed of. There are plenty of issues with trying to construct an empirical proof of God, many of which are inherited by Deists from Theists.
All empirical knowledge is hypothetical-contingent on various factors. This means that empirical truths are necessarily not apodictic truths. The previous statement is itself apodictic and non-empirical as it is necessarily true and does not have empirical postulates. Human Reason allows us to reason a priori, and we may use that ability to discern metaphysical truths beyond the realm of experience. I would not take seriously the claim that a bird both exists, and doesn't exist because that is logically contradictory even without attempting to empirically sense such a being. The case for God, and for metaphysical truths depends purely on a priori reasoning.