To me, they're not so much as 'mutually exclusive' but have nothing to do with each other as far as my perception goes. It may be different for you.
If you like I can give you my thoughts on religion and why I came to my conclusion. Religion and Politics are 2 dodgy subjects to talk about...
'Gods' existence is purely hypothetical based on written text.
Where the existance of God can be debated in a Metaphysical way I think the possibility of there being a 'Big Bang' belongs in the Physical arena.