If by "not mutually exclusive" you mean that the human psyche is capable of affirming two logically mutual-exclusives without being troubled by the contradiction, you of course are correct. Human mentality is capable of that, and a host of other evils. That is like saying, "It is possible to be a fiscal and social conservative who feels that a totalitarian state controlling all of human life and commerce, and crushing out every last vestige of human freedom, is the best form of government."
If, however, you mean that it can be done consistently with one's professed faith — that is, with the Bible — then you are mistaken.
I'm responsible for loading the bases--one out!
Then I am indeed a "cracked pot", because I find no contradiction between my faith and my science (and yes, I do actually read my Bible with great regularity).