To assert that science and religion are incompatible is partially true, but is also in a big way false. It is like saying science and history, or history and psychology are incompatible and incapable of being studied in communion with each other. In one sense they are incompatible, in that each are separate fields that have certain requirements of study that are unique to each. However you cannot say that they never cross.
To illustrate the different methods of inquiry, let’s take science and history. The scientific method is based on repeatable experiments. History, on the other hand, cannot be studied in this way because history is already in the past, and past events cannot be repeated as they first occurred. They can only be studied as past events. The evidence that supports a historical event is therefore different from the evidence that supports a scientific theory. This does not keep you from studying, say, the history of science (as an example of the two colliding), but my point is that the two fields have different methods of inquiry within their different contexts.
For the question of science and religion, these too have different methods of inquiry. The scientific method is different from the philosophic method just as materialism (the belief that matter is the highest state of being) is the opposite of idealism (the belief that the mind and its thoughts are the highest state). But the God of the universe created the laws of physics as well as minds suited for scientific inquiry. The Bible says that creation points to God the Creator. At the same time God transcends creation, and in that sense science is outside the realm of the study of God. We can look at the philosophical evidences for God’s existence, and the scientific and materialistic things that exist and point toward God. But God transcends both materialism and idealism because God transcends both matter and mind, being the Creator of both.