There's been a bunch of stuff flying around the net recently following the "debate" between John Haught (Catholic theologian) and Jerry Coyne (Evolutionary biologist & atheist). I am yet to watch the video, although I intend to, but I thought I would add my twopenneth to the discussion. (It will be interesting to see if I feel the same way after watching the video.)
My initial thought was that I felt a little uncomfortable with this topic as a debate - although upon further reading it seems that it wasn't really meant to be a "debate" in the usual sense. Nevertheless, there was a "for" (Haught) and "against" (Coyne) position. This implies that the answer is "yes" (they are compatible) or "no" (they are not). This, I feel, is a mistake. The answer depends on another question: which religion?
From what I have read, Haught seems to pull out some fairly standard arguments about "different types of explanation" (how versus why). This only holds if there really are different levels of explanation for the phenomena being discussed, although this weakness in the argument can be ignored when one is only interested in compatibility. Even assuming that there are different levels of explanation for the Universe (there may be no "why"), however, this only allows compatibility if the religious position stays in its different realm and does not encroach into that of science - the what and how. (Actually, I think science can sometimes also answer the "why?" questions but probably not all of the "why?" questions that religions and philosophy attempt to address.) In other words, this holds true all the time that religion is not interventionist - if god leaves no trace.
Science and religion are compatible in the sense that one can conceptualise a scenario in which a deity exists and science does not know/care. I believe it's called Deism. (One can conceptualise them, yes, but conceptualisation does not make them true.) One can also conceptualise a different scenario in which god is regularly intervening, performing miracles, healing the sick etc. This type of god would leave traces that are in the realm of science to detect - traces that we simply do not see. (As an extreme case, think Young Earth Creationism.) These religions are not compatible with science, without a lot of intellectual gymnastics that raise serious questions (for me) about the nature of such a god.
The important thing is that not ALL religion is compatible with science and, for me at the least, the religions that ARE compatible are largely pointless and/or irrelevant. I'm yet to watch the video (although I will) but it sounds like Haught knows this and is playing the game of talking about a deist-like non-interventionist god, while at the same time trying to imply that is is also true for other religious positions, such as Catholicism. (I don't mean to pick on Catholicism, it's just the one that Haught is associated with.) From what I have read, he gets caught on this in the Q&A and has to reject Catholicism (in essence, if not explcitily) to maintain his position.
It is right to attack his defence of universal compatibility and force him to explicitly recognise that not all religions - including most of the major ones - are compatible with science. On the other hand, I think the atheists need to be careful too. In "The God Delusion", Dawkins defines "God" (and hence religion) in a very particular way - Deist gods are excluded. (Who cares, or can say anything, about a god that does nothing?) This is useful for such a book and enables reference simply to "god" or "religion" but when targeting the wider population with the notion that "religion and science are incompatible", one has to remember that this is only true for some (albeit probably most) religion. Otherwise, one paints oneself into an uncomfortable corner where on has to start attacking legitimate (if, arguably, pointless) positions to maintain an over-zealous statement. (As I say, I have not seen the video yet, so I am not suggesting Coyne does this. I have seen it happen on discussion boards etc. though.)
So, are science and religion compatible? I think they can be but, personally, I would seriously question the value of the religion that was. If other people choose to believe such things then that, of course, is their decision. And here lies another area where I think atheists need to be careful. A lot of religious folks just don't care whether their religion is compatible with science. They don't care if their religion is apparently logically inconsistent. It's all part of the great "mystery" and not meant to be understood. This is not a position that I myself could maintain but they are not me. Furthermore, as long as they are not trying to structure society, impose moral values, or educate children based on these beliefs, I don't care what they want to believe.