Please do read The Dancing Wu Li Masters by Gary Zukav. Science today relies on a whole bunch of empirical constants that cannot be explained. Similarly there are a bunch of theories that are lacking proof but they seem to make sense in an “empirical” manner. Various Physical Constants, Gravity, Dark Energy/Matter, and Evolution are classic examples. Then you have situations such as the proved duality of mass and energy and the fact that anything with mass has a corresponding wave function. While this has only been demonstrated at the level of elementary particles extrapolating that to complex beings such as ourselves means that wave functions corresponding to us could be stretched across infinity and the simple concepts in wave theory can provide credence to the concept of an eternal soul. Imagine that our physical existence is a short manifestation of the wave function for a relatively short piece of space-time.
So while there is duality that can be sought between Science and Religion the trouble is the dogmatic nature of religion that has no equal in science. To believe and to have faith are absolutes that define peoples existence whereas as per science I have no idea as to how I even get my mass let alone how I can compose this response. So to be a person of science is to constantly question the ground that you stand upon whereas to be a person of religion is to worship and have absolute faith in an unknown force which supposedly has a grand design.
In conclusion, they are not two sides of the same coin and can exist independently of each other without any issues.