The Christian should question the person about this. We can point out that if there's no objective, fixed truth, all meaningful conversation will grind to a halt. If nothing a person says can be taken as true or false in the normal sense, the listener won't know if the speaker really means what he says. What would be the value, for example, of reading the cautions on a bottle of pills if the meaning and truth of the words aren't set? Trying to communicate ideas when truth and meaning fluctuate like the stock market is like trying to nail Jell-O to a wall. There's no way to get hold of any idea with which to agree or disagree.
The non-believer might object that not all matters are relative, only matters of religion and morality. However, the burden is on the relativist to prove that matters of religion and morality are relative, for it isn't obvious that this is so. Why should these matters be treated differently with respect to truth than others? The fact that one can't debate morality on the basis of evidences as one would, say, a scientific issue doesn't mean that the truth about it can't be known. More important, however, is the fact that Christianity in particular is tied very tightly to historical events which are matters of fact.
Christianity can't be true for one person but not for another. Either it is true and all should believe; or it isn't and it should be discarded.
One objection we hear is "Your values might be right for you, but they aren't for me."
First, we need to understand the historic Christian view of morality. According to Scripture, morals are grounded in God. As God is unchanging, so also is his morality. As Paul Copan notes, such morals are discovered, not invented. They are objective; they do not come from within you or me, but are true completely apart from us.
Having abandoned God as the standard for morality and replaced him with ourselves, some say there is no objective morality. When told that a certain individual believed that morality is a sham, Samuel Johnson responded, "Why sir, if he really believes there is no distinction between virtue and vice, let us count our spoons before he leaves." Johnson's quip doesn't prove that morals are objective, but it indicates how we'll have to live if they aren't. If matters of morality are relative, how can we trust anything another person says about moral issues? For example, if a person says that you can trust him to hold your money for you because he is honest, how do you know whether what he means by "honest" is what you mean by it?
But is it true that moral standards are culturally relative? Or perhaps the better question should be, Is it really likely that the non-believer believes this himself? You might recall the Women's Conference in Beijing several years ago. Representatives from all over the world gathered to plan strategies for gaining rights for women who were being oppressed. Could a cultural relativist support such a conference? It's hard to see how. Cultural relativism leaves a society with its hands tied in the face of atrocities committed by people of other cultures. But we know intuitively that some things are wrong, not just for me or my culture but for all peoples and all cultures. To take a firm stand against the immoral acts of individuals or cultures one needs the foundation of moral absolutes.