The two disciplines start with different and incompatible perspectives.
This sentence lacks scientific proof and thus is itself an unscientific proposition.
For being incompatible, it does not suffice that two perspectives are different. They have to contradict each other. This is not necessarily the case with science and religion. Science can be and is compatible with religion; it only is not compatible to _any_ religion.
In the beginning of mankind, science and religion were indiscernible. The first religious world views attempted to explain the world - just what science does. The first astronomers were priests, astronomy was a religion. Science and religion had the same roots, they only developed in different, but not necessarily incompatible directions.
Religious ideas that were indeed incompatible with science only came up much later - such as the idea of a dogma. If a religion has the dogma that the earth was created in six days, it has certainly a big problem with science.
On the other hand, modern Protestantism for instance does not contain dogmas and thus is compatible with science. Some people consider Atheism a religion. If that is the case, then it's a religion that is also compatible with science.