The secularization of culture happened as soon as Adam was thrown from the Garden for eating forbidden fruit. He had sinned, and cut off from direct union with God human civilization became a largely irreligious affair—Christians have been trying ever since to increase their influence in the arts, politics, academics and the popular sphere.
To hear a lot of modern apologists, however, you'd think the shift away from historical Christianity to worldly attitudes was recent. Some look back as far as the Enlightenment, some as little as thirty or forty years ago, showing how political and moral trends evidence the departure. For them, the real bad guys are Charles Darwin, Friedrich Nietzsche, Jean-Paul Sartre, sometimes even Soren Kierkegaard (one of the really great Christian writers of the last 200 years).
While those outside the Christian tradition could perhaps be forgiven such shortsightedness (intent on tracing Modern Progress as they are), for Christians to share these views is unforgiveable. Western civilization can be traced to ancient Greece, and before that to Egypt, two of the most pagan and corrupt cultures of all time. The ideas popular now have their roots in the philosophies of Plato, Aristotle, Zeno, Democritus and Thales.
Every modern philosophy has a Classical era corollary, if not its direct match at least the primitive form of the current idea. Anaximander suggested men evolved from animals 2500 years before Charlie Darwin was born; Heraclitus posited rudimentary postmodern philosophy two millennia before the advent of modernism; Diogenes was a nihilist before the nation of Russia existed, and about 300 years before Christ.
The best way to understand 20th century literature is not as a brand-new canon promoting recent anti-Christian thought, but as a body of work manifesting the newest iterations of secular philosophy and Christian responses. Great writers of the past, from Shelley and Robert Louis Stevenson to Rabelais and George Eliot, were fully as secular (even atheistic) as any Hemingway, Camus or Douglas Adams of the last 100 years.
Just as secular—and in many instances, just as brilliant. While there's more bad writing available than ever before as a result of the democratization of publishing, for every Stephanie Meyer there's at least one Faulkner or Annie Dillard. The novel came into its own in the 20th century as writers understood its limitations. Good writers have something universal to say about humanity, avoiding merely regional or too-specific interests.
Not all of it is "fun" reading—some of the best writers like Kafka, Thomas Mann and Solzhenitsyn can be hard to get through, though they can also write riveting passages of elegant prose. Others are a joy to read, like Steinbeck, G.K. Chesterton and George Bernard Shaw, combining a talent for poetic narrative and humor reminiscent of Dickens and Twain.
Like the ideas it embraces, the purpose of 20th century literature remains the same as the literature of any other era: to examine life, to celebrate it, to understand it better, and to connect readers with each other and with new ideas. Of course you'll want to be aware when you're reading secular authors and examine their work closely, but the same is true of Benjamin Franklin's Autobiography or Virgil's Aeneid.
Most of all, enjoy these books. The best of them explore deep and important ideas, but the best of them are also great artistic achievements, not mere dissertations but independent organisms alive and dangerous and beautiful. For all the technology and machines of our modern age, good literature is still organic, and the ability to enjoy it comes from an unmapped region of the soul where every Kerouac, Cather and Marquez had to go for their masterpieces.