Put the question this way: What are the values that Western democracies cherish? At a minimum they would include:
- Human equality (including that of women and minorities) under the law
- Tolerance of dissent
- Separation of church and state
- Social Justice (charity, concern for the poor)
- Freedom of speech
- Freedom of religion
Nor does naturalism (the worldview held by many secularists that says that the natural world is all there is) offer any support for any of these. On naturalism we are the product of blind, impersonal forces that have shaped us to survive competition with our competitors. There is nothing in this process which in any sense mandates any of the values listed above. There's no reason, on evolutionary grounds, why any society should value any of them over their contraries.
But, it might be argued, evolution has equipped us with reason, and reason dictates that these values afford the best way to order a society. We don't need Christianity to instill or ground these values, according to this argument, reason can do the job.
This, however, is simply not true. Reason can perhaps help us find the best way to exemplify these values, but it cannot decide whether or not a society should incorporate them. To prefer a society which upholds them over and against one which does not is simply an arbitrary preference. It is to say that a society which exhibits these values is better than alternative polities because, well, most of us just happen to have a fondness for these values.
Moreover, aside from providing a solid grounding for those political values, Christianity bestowed additional blessings on the West. There's a consensus among scholars that the vast majority of the world's best art and music has been inspired by Christian assumptions. These also furnished the motivation for the development of schools, orphanages, hospitals and charitable organizations throughout Europe and North America and provided the fertile philosophical soil in which modern science could germinate and thrive.
To the extent that other worldviews have inspired their followers to notable cultural achievements, generally speaking they have neither amounted to much nor been sustained for long without somehow piggy-backing on Christianity.
Naturalism and Islam may some day succeed in extirpating Christian influence, but the world they would create will look very much like either the Stalinist dystopia of Orwell's 1984 or the Islamic dystopia of ISIS. It might not happen abruptly - an airliner can glide a long way after having exhausted its fuel, and the higher its altitude the longer it can remain aloft before crashing to earth - but it won't remain airborne indefinitely.
Similarly, one or the other of these two bleak dystopias represents the future that awaits us a generation or two after the fuel of Christian assumptions has finally been drained from the West.