In Mere Christianity, C.S. Lewis speaks about the central claim of Christianity as being the person and work of Christ, especially his death and resurrection. Lewis came up with his famous trilemma of liar, madman or God, which as an apologetic tool works great in the remnants of Western Christendom in proving the divinity of Christ and calling the individual to a response to the claims of the Christian faith. Its simple presentation is powerful in its simplicity, which is one reason why Lewis, although not an Evangelical (he has some really questionable doctrines) is so popular among Evangelicals.
As the plates buckle and shift under the ground of Western civilization, the common Christian assumptions behind Western Civilization will increasingly whither and become obsolete. In an increasingly neo-pagan culture, common arguments for the Christian faith lose their power. This is especially seen in non-Western settings, whereby even traditional arguments for the Christian faith were not very persuasive in the first place. These arguments however could work as countries embraced Western learning which still has an echo of Christian thought. It is not surprising that those most susceptible to the Gospel tend to be upwardly mobile people educated with a modern Western education, while those stuck in traditional thinking prove more resistant to the Gospel.
Wherein lies the difference except in the Christian foundations of Western civilizations with its Christian cosmology? Even with the rise of Darwin, Christian cosmology was the target for people from Lyell to Darwin to Huxley. They rejected it consciously for an alternative, but even then their thought patterns were shaped in reaction to it. But what happens when those stories leave the mindset of the culture, such that people do not react against it as much as discount it totally or are ignorant of it?
If Genesis were false, if the Genesis cosmology is not the default, then traditional apologetics and even the Gospel presentation suffers. To illustrate this, I use Lewis' trilemma. Subtract the Genesis cosmology, and Lewis' trilemma becomes irrelevant. So Jesus is God? OK, so? The "westerners" can have their "Jesus" God, and we have our own deities and gods. You claim that Jesus died for sins. That's nice, but there are more ways to take care of sins. Yours is just one way, more for "westerners." But you say, Jesus proved his claim to be God and thus his exclusivity also, in his resurrection. I'll respond, all this happened in the context for Jews and the Westerners who follow them. It doesn't apply to me, since I see no [insert any non-Western ethnic group] mentioned in the Bible.
If Genesis were false, if it was not literal, I see no reason why Christianity is true for me. All apologetics will fail, because the Christian faith can never take root where its claims are relativized and rendered irrelevant by foreign cosmologies. And this is why the creation-evolution controversy is so vital to the church today.