Most public debates in America produce more heat than light. One of the most heated of those debates is the debate known as "Science versus Religion." The basic tenet of the extreme advocates for "science" is that science is not only incompatible with religion, science has proven religion to be false. Some descriptions of the debate actually presuppose the answer given by the extreme advocates of science. E.g. "Faith versus Reason" (presupposing that those who have faith are unreasonable). My favorite warped description is "Brights versus Dims." This presupposes that those who advocate for a Godless science are "bright" while those who believe in God are "dim." Of course, such a dichotomy classifies Rene Descartes, Galileo, Copernicus, Isaac Newton, Augustine of Hippo, and Thomas Aquinas, to name a few, as intellectually challenged.
Science cannot disprove religion. The scientific method presupposes that all phenomena have natural explanations. Science therefore refuses to consider supernatural explanations. It is impossible to disprove what you refuse to consider. What science can do, however, is disprove specific historical and scientific facts which have been taken as articles of faith by certain religions. E.g. The science of botany has shown that the mustard seed is not the smallest seed. (See Mark 4:31).
The core belief of monotheistic religions (that there is a God who created the Universe) cannot, however, be disproved by science. The belief is actually irrelevant to the scientific method for the reason already stated: Science refuses to consider supernatural explanations for anything.
Naturalism, the refusal to consider supernatural explanations, comes in two flavors--methodological and philosophical. Methodological naturalism recognizes the possibility of supernatural explanations but refuses to use them because "God did it" isn't a very satisfactory explanation for questions like "How does an internal combustion engine work?" Many scientists are both theists and methodological naturalists. Philosophical naturalism denies the existence of God and refuses to recognize the possibility of supernatural explanations. Philosophical naturalism is therefore basically atheistic.
The battle is therefore not between science and religion but between religion and those philosophical naturalists who seek to employ science as a weapon against religion.