Well, my two cents is that science and religion do peacefully and harmoniously co-exist for me. They are not the same, but they overlap without doing one another any discourtesy. In applying medical science, I find that the principles of Druidry help me to focus, to draw strength from what is greater than myself, and so forth. I also find that what I learn on a spiritual level has a level of agreement with science; if it doesn't, I throw it out.
I believe that science is a methodology designed for this realm specifically; it understands and applies natural laws as far as it is able to. It is designed to answer certain kinds of questions: what and how in particular. Religion to me is designed to answer other kinds of questions: why and who in particular.
I believe that science indicates the flimsy nature of this realm, and points to a much deeper reality. Atomic theory, for instance, reveals that what appears solid and static to our eyes is in fact largely empty space and constantly in motion. In other words, our 'reality' is in fact largely 'illusory'.
Science tells us that the Universe is made up of matter and energy, which can be neither created nor destroyed. Matter, in fact, is a form of energy itself. We are quite limited in our understanding of energy; but we know that there is a wide variance in type and application of energies. The old dualistic paradigms have been thrown out: the old argument over whether light was particle or wave is obsolete, because now we know it is, in fact, BOTH.
Given the fact that in applied sciences (such as medicine, my own field) we *MUST* keep in mind that what we know is flexible, constantly growing and prone to changes - even total about-face changes - I find it a little arrogant when people use science as the sole trustworthy measuring stick for Truth. Science does not measure truth; it measures certain qualities and quantities we have assigned to this natural world we live in.
There is evidence apart from the scientific kind; in a courtroom, for instance, testimony is accepted as firsthand evidence. In fact, the testimony given by a witness is quite valuable. In religion or art, I call this kind of evidence experiential. I think the two situations are comparable because what is being measured in both cases is one person's *perception* of what they see, hear, touch, smell, taste, and otherwise experience. It is of necessity subjective; in a court this is recognized, and it is understood that what the individual witnessed is not NECESSARILY the exact truth of what occurred, but is their perception of events. Perception varies from person to person, but its variance does not discount it.
I believe in reincarnation - why? Because Delilah the Fortune-Telling Psychic told me so for a mere $19.99 on my MasterCard? No. I believe it because I have experienced what I perceive as past-life memories, and because in observing nature I see spirals everywhere; from galaxies to seashells. We are always circling, repeating a pattern, yet progressing to some eventual goal. Morning becomes noon becomes night becomes morning; Winter becomes spring becomes summer becomes autumn becomes winter. The plants spread their seed, die, and are reborn, then grow to spread their seed, and die, and are reborn.
Is that sufficient evidence? It is for me. It is not for many others, and I have no problem with that. It doesn't bother me if you find reincarnation to be an unrealistic concept that has no relevance to you personally; just don't get on some high horse and try to tell me I'm silly because I find it a realistic concept that DOES have relevance to ME.
Science does not have anything to say to religion in some areas; in the areas in which they do meet, I find them congenial. When and if they disagree, I have always sided with science, because this is the realm I am in and this is the place I can learn most about universal law. I do not believe in the supernatural; I believe all things are natural, but much of nature is still beyond the scope of science. I don't think it will always remain so, but for now it is. And that's perfectly OK with me.