There are several ways science and religion can be in conflict.
If, say, one literally believes the world began sometime in the last 10,000 years as described by Genesis, the conflict is fundamental and irresolvable.
If one believes for religious reasons that God intervened miraculously at crucial moments in the history of life, ala intelligent design, there is little science can do to prove you wrong. But what science can do is show that there is no need for such an hypothesis, that the appearance of complex life forms can be accounted for by natural processes. The conflict here is not with the content, but with the spirit and method of science.
What about those matters that seem essential to many people of faith: the miracles of Jesus, his resurrection, the immortality of the soul, etc.? Again, one can choose to believe these things as a matter of faith and there is little science can do to prove you wrong. But there remains a conflict with the spirit of science, which has shown remarkable progress in explicating the world without invoking miracles. What science can show is that similar beliefs are common in many faith traditions and can be accounted for culturally. What science has done is show that whatever it is we can empirically call the soul is inextricably embedded in body. What science can do is show that none of the defining miracles of the world's faith traditions meet even the minimum evidentiary requirements of science.
Anyone who embraces the spirit of science -- and the powerful tool of Occam's Razor -- must naturally be skeptical of the miraculous claims of religion, which undoubtedly explains why so many scientists count themselves agnostic or atheistic.
But the fact remains that we find ourselves in a world shot through with mystery, and that the more we discover about the world the more profound becomes our sense of the world's grandeur and our own ignorance. In addition, an itch for self-transcendence seems to be part of our human nature. Strip religion of the historically contingent, the miraculous and the sectarian, put away the gods and spirits, and there is still ample room for awe, mystery, attention, praise, which is why many of us who embrace both the content and spirit of science think of ourselves as religious.