We should agree on what is meant by a terms such as 'science' or 'religion' when we compare them; broadly, there are two meanings. Firstly, they each refer to a set of truth claims made about the universe; gravity behaves in some way, or Jesus Christ performed some miracle, for example. Secondly, they represent an approach or a methodology to understanding the nature of the universe and our place within it. That is, they both give methods, such as the scientific method or biblical canon, by which we are to understand the universe about us. There is thus both sets of facts and, secondly, methods by which one determines these facts and we can compare science and religion in either of these ways.
Whether science and religion are compatible in the first sense, as sets of truth claims, simply rests on whether the two each make some claim that is fundamentally incompatible. It depends on what exactly is being claimed and, while this is relatively clear for science (one is referred to major scientific journals), it is somewhat less consistent for religion. For example, someone who believes in young earth creationism that the universe was created perhaps 7000 years ago is making a truth claim about the age of the universe that is in direct conflict with the truth claim offered by geologists. Only one can be correct and the scientific claim and the religious claim on this issue are fundamentally incompatible.
Now take the other extreme where, instead of offering a claim with a clear and indisputable violation of science, the religious claim is essentially unfalsifiable by science. For example, a deist might claim that all the universe is precisely as science says it is, but that the universe itself was created by the deity to be as it is. This is a claim that, by definition, is not disputable or directly on contradiction to science. I have a philosophical argument, expressed here, which argues that such claims are invalid because they are essentially vacuous and it is only through linguistic tricks that they appear as anything else. Regardless, there is not a direct contradiction between science and religion in this case.
I will expand on the question of the compatibility of truth claims further below, but let me first pause to note that any such discussion just focusing on the truth claims would always be incomplete. However compatible or incompatible the specific sets of claims about the universe are, there is a much more fundamental way in which religion and science are innately incompatible. That is, we turn to the question of how compatible the approaches and methodologies of religion and science are to understanding the universe.
In science, one begins by asking questions. In religion, one begins by stating the answer. In science, skepticism, uncertainty, and doubt remain not just incidental but absolutely core to the basic methodology and epistemology of science. In religion, absolute certainty is both demanded and expected to the point that strength of conviction, not strength of skepticism, is valued. In science, the strength of a claim is measured based on evidence and reason and is quickly discarded if found lacking. In religion, the strength of a claim has no modulation; if it is stated by the religious canon then it is considered fact.
These are not incidental differences. These are differences at the very core of comparing science and religion. They are not merely different, the are diametrically opposed and fundamentally in conflict with each other on the question of their basic methodologies to understand the universe. This is a tension too great to hope to be resolved without one side sacrificing its very core. In time, major religions may, as they already are, abandon claims in the scientific domain such as the question of evolution. But in thousands of years, they have not abandoned the way of understanding the universe that is fundamentally opposed by science. Whatever the differences in the sets of truth claims are, the differences in methodologies to determine truth are fundamentally incompatible with each other.
In some sense, it is misguided to even think of science as a set of facts or claims about the nature of the universe. At its core, science is a methodology and its core canon is the scientific method. The set of commonly accepted scientific facts is modulated based on the results of the scientific method and, as scientific history has shown, the claims of the movement always plays a deferential role to the primacy of the methodology and, indeed, have no strength without it. In contrast, at its core, religion is a set of claims (such as that God exists) and is only a methodology for determining truth statements by inference. To compare, as I did above, first the two sets of claims and then the two methodologies, is to act as if either comparison is equally valid. I find the comparison of methodologies to be far more important and the comparison of the sets of claims to be distinctly secondary. This is for the simple reason that a good methodology, by definition, ought to be better at producing true sets of claims. By placing more importance on methodology, science thus begins with the advantage.
Returning to the question of comparing the sets of truth claims, I submit that most contested points between religion and science that have survived the test of history and remain today are one of the two extremes that I gave examples of earlier: clear violations of science, or vacuous and unfalsifiable assertions. For example, consider the claim that Jesus performed miracles such as walking on water. This is a clear violation of physics if one assumes Jesus and his influence on earth behaves according to our understanding of physics. If, however, one postulates that Jesus is not bound by such laws and that there is some form of supernatural explanation then this is not a contradiction with physics, by definition, but it is entirely unfalsifiable and thus vacuous.
A large part of the problem of finding direct contradictions between science and religion is that we cannot find these contradictions in the sense in which science considers things to be a contradiction. The reason is simply that the concepts espoused by religion are often sufficiently vague and poorly defined that scientific contradictions are not possible. Take, for example, a scientific prediction in particle physics that some particle ought to have some mass. This is a very concrete prediction, and a test can either find it correct or incorrect in which case we will say there is a contradiction. In religion however, there simply is not sufficient concreteness to the concepts to be able to speak about them cogently. It is thus not a point in religion's favour that science and religion for the most part don't have clear and objective contradictions, for this is do not to the fact that they are intrinsically compatible concepts, but to the fact that we cannot speak about religion in a sufficiently meaningful way as to find it in contradiction with science. Even the most basic concept in religion of a deity is usually only vacuously define, usually in a self-referential way.
While the domains of knowledge claimed by religion have shrunk over time, currently the biggest point of contention is, of course, evolution. Claims on behalf of the religious community vary from claiming that evolution of any form is impossible, to imposing a (false) distinction between so called micro-evolution and macro-evolution, to arguing that evolution needed a deistic kick start instead of abiogenesis. For the most part, however, I think a careful analysis of the level of evidence we have for evolution demonstrates that all but the last of these is a claim in direct contradiction to a claim from science. Indeed, many in the religious community are happy to accept that there is indeed a contradiction between science and religion on this point and believe that they are correct. However, issues like this are actually relatively rare that provide clear violations between the religious community and the science community on an issue that is a priori falsifiable.
I think it is fair to say that today most truth claims about the nature of the universe are not ones that directory and obviously conflict with science, with the exception of evolution. We might be tempted to think, therefore, that the gap between science and religion is not very large for there are not so many spots of direct conflict, and while the methodologies may be different, the sets of truth claims are not so incompatible. However, this has not always being the case as the story of Galileo so poignantly reminds us. The reason that religion does not dare utter direct contradictions to science outside of evolution is that they have consistently shifted their views throughout history to adjust to whatever it is that science says. Sometimes there is a lag, but in the broad view it has been a capitulation of religion to science every time and never the reverse. It is a false illusion of compatibility on the truth claims question because any compatibility has not arisen from a fundamental compatibility between the two methodologies, but from capitulation of the one to the other every time they substantially differ.
Finally, I will note that the claim "there is no deity" is not a scientific claim. It is a philosophical one. Silence correctly says nothing on the topic of whether there is or is not a deity (and thus says nothing on the various unfalsifiable claims made by religion) because there is simply nothing to say if one has no evidence in the scientific method. There are many interesting philosophical questions in epistemology and ontology that get at issues such as whether we should accept unfalsifiable claims as meaningful. I think these philosophical arguments are fairly strong for a natural materialism position, but this is not the subject of this post. Such philosophy makes claims that are in considerable tension with the claim "there is a deity" but at the scientific level I will maintain that science is not fundamentally incompatible with the majority of claims of religion outside of narrow topics like evolution or the age of the universe.
I think this issue can be an effective tool to demonstrate the failings of religion. As mentioned, most people do value science and the scientific method. Few would claim there is something fundamentally wrong with the ideas of needing evidence to believe claims in any discipline except religion. Because there already is this innate appreciation for science, half our work is already done for us in persuading people. However, if it is left standing that science and religion are indeed compatible, then people will not experience any tension between the two. It should thus be pointed out, along the lines of the above, that at any important level they are not compatible. One has to make a choice between the two if one wishes to maintain intellectual honesty. When so framed, I don't see how this could be anything but a trivial choice.
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