How might some common doctrines and beliefs bandied about by Christians be evidence of crypto-atheism?
One example. One of the clichés many believers toss merrily about is that evolution is how God created. Science can only study the mechanisms by which God acts and not the hand of God itself in the material world.
First, implied in this answer is that there is no evidence, or at least no unambiguous evidence, for God acting in the world. Appeals to evidence indicates an empirically-minded approach to the problem of God in the world. God is not a scientific hypothesis. Consequently, God is superfluous to science.
If God is superfluous to empirically-minded investigations of the world around us, of what use is God, if He does not help us understand the physical world? God, one might say, is not in phenomena. Assertions of God's existence do not indicate any new truth or further understanding of what an empirically-minded person might investigate, rather such assertions are rooted in the needs, desires, and fears of the person making the assertions. Consequently, God is a psychological phenomena.
I suspect that people who believe that God acts in history believe that God acts in the same way that I do when I move my hand. God acting in the physical world is an assertion of will. It would be consistent to believe that so-called physical laws are a figment of human thinking: positing hard and fast relations where there are in fact none. Moment to moment all of Creation continues to exist at His behest. The physical world would not exist independently of His Will.
In order for God not to be eventually made superfluous to an explanation of the world, God must absolutely and without reserve provide for the continued existence of all physicality.
Of course this means that the religious-minded would be absolutely indispensable. The religious-minded would have no need of knowledge of illusory physical entities. The religious-minded would know of things far, far more important than the illusions of mere matter. Their ignorance of physicality would be an asset.