I find that they can
co-exist. Science cannot currently explain everything, hence, you can have faith in something. Science and religion may indeed say opposite statements, however, there is no reason why you cannot have both. Science is to be analyzed by science whereas religion is to be analyzed by religion. If you keep them separate, then there is no problem. However, many people don't and try to mish-mash them together and that is where the large mess occurs.
You don't adopt the biological paradigm and then try to mix that with the psychodynamic paradigm yet keep them separate at the same time. If you do, you're very likely to get some big mess, which is the same for science and religion.
People feel some need to try and put the two together in some obscure hope and then they get the big mess. But give a simple analogy of apples and oranges and that makes sense... .
If you begin comparing science and religion, the two have different viewpoints, follow different paradigms, what is the expected outcome(s)? To show one is "better"? Time and time again, it ends with people describing what science and religion are, and assuming they understand them both, they smash them together once again.