What? You are assuming science and religion are the same kinds of things.
Not exactly. I'm assuming "the belief that science can describe an objective, external world" and "the belief that an objective, external world exists at all" are the same kind of "the belief that God exist".
True, science is a method to study the external world; but you can also see religion as a method to study emotions and human relations. You can use religion to make assertions about reality in the same way that you can use science to make moral judgements - which is, by stretching the method outside of their area of validity.
Being beliefs, neither can be proven nor disproven merely by logic alone; beliefs are ultimately based on emotion, not reason. In that level, yes, they're the same kind of thing. I may believe that science is a better method to learn about existence, and I may even believe that it's incompatible with religion, but I can't prove it scientifically; that would be an infinite recursion.