It's fair to say that the science organisations have taken policy stances that science and orthodox religion are not incompatible. In my view, that is a deplorable step. At stake here is a profound and controversial philosophical question: is the emerging scientific image of the world compatible with any of the religious images of the world that are currently on offer, particularly those that claim to be orthodox? Individual citizens are, of course, quite entitled to have views on that question. Likewise, as free citizens, individual scientists are entitled to have their philosophical views. However, it's not an issue that can be resolved within one specialised science; nor can it be settled by the policy decisions of one or more science organisations. It requires an analysis of the worldviews offered by various religions, including a consideration of which doctrines are considered essential by religious authorities and which are more peripheral. These must then be compared with the overall picture of the world in space and time emerging from scientific investigation. This involves an assessment (based on the consensus of scientists in the relevant fields) of which theoretical propositions are so well-corroborated by now that there is little prospect of revision, even though no scientific claims are considered certain or totally beyond revision. In other words, we need to assess which propositions should be considered established findings. Comparisons must then be made between essential religious doctrines and science's established findings.
In the end, reasonable people may differ about whether there is any incompatibility, though I am convinced that there really is an incompatibility between important, orthodox positions in Abrahamic theology, on the one hand, and established scientific findings on the other.
Before getting to that, I should note that some religious positions are plainly incompatible with well-established scientific findings. The image of the universe in space and time that has been built up by the converging investigations of scientists in such fields as geology, astrophysics, and evolutionary biology was not contrived for the purpose of discrediting religion. Rather, it is the gradual result of ordinary methods of rational inquiry supplemented by more precise methods that have become increasingly available since the time of Galileo — such as instruments that extend the human senses, mathematical modelling, and apparatus that enables many decisive experiments to be done. As a result of patient scientific work over the past few centuries, increasingly specialised and professionalised in recent decades, we now know that the universe we live in is billions of years old, that our planet itself is something like four-and-half billion years old, that life diversified through an evolutionary process involving mechanisms that prominently included Darwinian natural selection, that our own species, Homo sapiens, first appeared in Africa about 100,000 to 200,000 years ago, and so on. However, some religious leaders teach that our planet is only about 6,000 to 10,000 years old, that biological species have not evolved from earlier species, and so on. Given the overwhelming scientific evidence against that image of the world, all such religious doctrines are plainly and directly at odds with well-established outcomes from rational inquiry.
More importantly, however, at least for those of us who live outside of the United States with its abundance of creationists and the like, the scientific image of the universe is difficult to reconcile with more general ideas from traditional Abrahamic theology. It is particularly difficult to reconcile the scientific picture with the existence of an all-powerful, all-knowing, loving, providential deity, seen as the creator and sustainer of the universe. Note, however, that this "difficulty" is a philosophical inference, reached after a process of comparison between Abrahamic doctrines and scientific findings. It does not amount to a plain contradiction between religion and science, but is mediated by various assumptions that may (I'm willing to suppose) be debatable.
People like me - philosophers who are sceptical about the truth-claims of religion - may ask, pointedly, why an all-powerful, all-knowing, loving, providential deity has employed biological evolution to bring about rational life forms like us, assuming that that was the deity's goal. It would have been within the power of such a being to create us, just as we are now, in the blink of an eye; instead it used the slow, uncertain methods of mutation, survival, and adaptation. What was all that about? As I argue in my forthcoming Voices of Disbelief essay, such a being, whose attributes include omniscience, would have known that this process would lead to untold cruelty and misery in the animal world, imperfect functional designs, and a timeframe of billions of years for rational life to eventuate. In short, why wouldn't a superlative being, such as the orthodox Abrahamic God, simply have chosen the outcome it wanted - then made it happen? As the Koran says of Jesus' virgin birth, "When He decrees a thing He only has to say, 'Be,' and it is." So why all this suffering, wasted time, and imperfection?
In defending the compatibility between religion and science, orthodox Abrahamic theologians and believers must either abandon their orthodox views (perhaps moving towards deism, or some kind of process theology, or even to an irrealist/metaphorical conception of God); or else they need to offer theological propositions that reconcile God's providential love (and other attributes) with the choice of such methods of creation. I very much doubt that the latter can be done in any plausible way. The attempt to reconcile orthodox Abrahamic religion with well-established scientific findings leads to unbelievable intellectual contortions.
But what if I'm wrong about this? Perhaps there are Christian (or Jewish, or Islamic) philosophers who can answer the point I'm making. Well, fine. But even if there are, official organisations representing science don't - or shouldn't - get to adjudicate between them and me. This is a highly contentious issue that falls outside the expertise of such bodies.
In any event, individual scientists are entitled to have views on such philosophical issues, and it's clear that many scientists take positions much like mine. Those scientists have every right to be angry that their official organisations - organisations that are supposed to be representing them - are taking a stand on the issue. This leaves aside the arrogance of science organisations appearing to favour particular religious viewpoints. Of course, it's true that some religious viewpoints are just irrational, in the sense that they plainly contradict well-established scientific findings. Others, even on my account, are incompatible with science only in relatively subtle ways, and reasonable people with those viewpoints could put some kind of case against my position (even though I might not consider that case to be at all plausible). While this is all true, it's not up the scientific organisations to be saying it. That's outside their remit. It’s really up to the religionists to alter their views to bring them into line with well-established science - if they can. Or they can choose not to and go on advocating positions that range from plainly irrational to (more) subtly implausible. They may even fight back with nonsensical pseudo-science such as warmed-over diluvian geology or Flintstones-style depictions of humans and dinosaurs sharing the same environments.
Science organisations should stick to the point that certain findings are the result of systematic, rational investigation of the world, supported overwhelmingly by several lines of converging evidence. In putting that case, they can be "religion blind"; they should present the evidence for the scientific picture, but that's as far as they should go. They should not comment on what specific theological positions are or are not compatible with science. Leave that to the squabblings of philosophers and theologians, and, indeed, of individual scientists or other citizens. We can think and argue about it for ourselves.