The obvious answer is no. A Christian doesn’t have to write overtly Christian material. My Phoenix Quest novels, as an example, are more allegorical of Christian truths than they are meant to be in-your-face-Christian. In such a case, the writing is not overt, but subtle.
However, as a Christian, I have the desire to promote Christian principles. I want my writing to uplift my Savior and expand the Kingdom of God within the kingdom of man. My goal is not to uplift me or worldly philosophies, but to uplift Jesus Christ.
I believe fiction can be a fantastic means of doing so. As a result, I wish more Christians would write fiction. Jesus used parables to promote truths, so in the same way, Christian authors can do the same thing.
My experience with publishers, for example, is that they are all about making money. In several cases with my books, they have tried to convince me to hide the Christian elements in an attempt to make the book more appealing to a broader range of people. This wasn’t an altruistic suggestion. It was to expand their ability to make money. And if you are all about the money too, then following such advice may seem a legitimate approach.
However, I’ve learned that niche writing seems to do better. For Christians, there are not tons of good, clean, well-written books out there. Christians crave wholesome stories that do not attack their values. With that thought in mind, I wrote the Davidic Chronicles, and the series, with a little promotion, has really taken off. Yes, I’m making money with the books, but I am more interested in providing wholesome content for Christian consumption.
Another argument against writing overtly Christian works is an effort to reach non-Christians. This is a noble goal, but I’ve found I have been more successful reaching non-Christians by simply providing fun, entertaining content where I do not hide my Christian worldview. In the end, you’re going to have to make your own decision.
In short, no a Christian does not need to write overtly Christian stories, but I do believe a Christian should honor Christ in everything he or she writes.