The problem is not so much that religion conflicts with science as it co-opts science. Evolutionary thinking was mandated by leading theologians and religious thinkers in the Enlightenment and Darwin's arguments for the truth of evolution followed suit. As David Masci, senior researcher at the Pew Forum, writes:
But although evolutionary theory is often portrayed as antithetical to religion, it has not destroyed the religious faith of the scientific community.
But this is not to say evolutionists are predominantly religious today. For Darwin, as Richard Dawkins famously put it, "made it possible to be an intellectually fulfilled atheist." Ironically, the religiously motivated and justified theory of evolution has fueled atheism and today the camp is split. Here there is a conflict as the atheist evolutionists and theist evolutionists argue about their differences.
But as Henry Kissinger described academia, the battles are so fierce because the stakes are so small. From the outside the conflict between atheist evolutionists and theist evolutionists is rather meaningless. For the atheists, in spite of all their bluster, are no different than the theists in their religious beliefs. They call themselves atheists, but their convictions about god are as strong as anyone's. (see examples here and here).
So yes many evolutionists are atheists, but as usual the theology rules. Evolutionists are either theists who hold strong religious convictions or atheists who hold strong religious convictions. Either way the science suffers. I guess you could say there is a conflict between religion and science after all.