America is one of the few places in the world with an ongoing public debate about the interface (conflict?) between science and religion. One of the problems with this debate is that debaters too often cook up questions and issues that serve their views without contributing to any enlightenment.
For example, there's the confusion between deism and religion. We might all be better served if the two terms were kept separated. They are not equivalent. The term "deism" should be used to refer to a belief in God (or Gods) and "religion" to refer to a social group with a particular doctrine about God (or Gods). The difference is critical, because many people are essentially deists without belonging to any particular religion. It's maybe unfortunate that too many people ask if science is compatible with religion when what they really mean is the question whether science is compatible with a belief in God (or Gods).
The problem for the working scientist is that the essence of science is a self-conscious and mandatory objectivity -- which means dogma and doctrine are essentially antithetical to science, not so much on philosophical grounds but on actual procedural grounds. In plain words, science requires objectivity and dogma is by definition an absolute enemy of objectivity -- and therefore an enemy of science.
In this context, the main source of dogma as an enemy of science is not deism, it's religion. A mere belief in the existence of God (or Gods) without any dogma about the natural world deriving from that belief is no practical enemy of science. In contrast, a strong dogma (doctrine) about the natural world derived from religion is nearly always antithetical to the practice of science.
We need to say "nearly always" because it depends on which science is in practice. Most religious dogma says very little directly about physics or chemistry. A particle physicist or a quantum theorist or an organic chemist who is a member of a religion usually has no religious dogma that constitutes an enemy of objectivity. The same is true of the engineering sciences. In contrast, a biologist, a psychologist, a social scientist, a medical scientist, are all very much aware of the conflict between religious dogma and the practice of their science. In general, the further removed a particular science is from human affairs, the less relevant to practice is any religious dogma.
A particle physicist does not need to make moral and religious value judgments about protons and gluons. In contrast, a psychiatrist in practice may have a difficult time separating his religious beliefs from his dealings with his patients.
So the question whether "science" is compatible with religion is a bad construction because in the context of the question the term "science" is ambiguous. Nevertheless, if we say adherence to any dogma is incompatible with any science (which is my own view), then the question is answered. My own view is that there is no room for any dogma in science -- no room at all.
In general, most scientists are professed atheists -- no belief in God (or Gods), although I'm not certain how the surveys handle the difference between deism and religion. About 90 percent of the members of the National Academy of Sciences are apparently atheists. Richard Dawkins is a celebrated public scientist-atheist. Thomas Paine, one of the Founding Fathers of America, was a celebrated revolutionary-deist. In contrast, Francis Collins, our new chief at the National Institutes of Health, is a practicing Catholic, and there are many thousands of scientists in America and elsewhere who label themselves as members of some religion.
What's usually missing in discussions about these questions are calm voices. The other day I received in the mail a book on the subject written in a calm voice. Fred Grinnell is an accomplished cell biologist who gives us a very readable little book: Everyday Practice of Science: Where Intuition and Passion Meet Objectivity and Logic. The first half of the book is about the daily practice of science, and the second half is about the interface between science and society, in particular the interface (conflict?) between science and religion. It's an intelligent and very readable book in a calm voice, and it certainly should be read by anyone interested in the ongoing (and raging) dispute about the compatibility of science and religion. Fred Grinnell is completely opposed to both Creationism and Intelligent Design, but he argues that science and religion are indeed compatible -- room for both. That's a viewpoint, and although I disagree with that viewpoint, his book is a smart book with a decent argument that deserves attention.
Frederick Grinnell: Everyday Practice of Science: Where Intuition and Passion Meet Objectivity and Logic. Oxford University Press, 2009.