It is completely acceptable, but in no way obligatory, for born-again Christians to say "Merry Christmas." Ironically, this question gets asked in two very opposite contexts. On the one hand, some people are concerned about the legitimacy of Christmas. They want to know if saying "Merry Christmas" is some kind of compromise. On the other hand, many American Christians are concerned about the cultural drift away from the significance of Christmas. For them, saying "Merry Christmas" is something that Christians not only can do but should do. It is a small but significant part of their effort to keep Christ at the center of the season. They see alternative terms like "happy holidays" or "season's greetings" as subtle methods of removing the name of Christ from the public square. I sympathize with both of these positions and admire the common reality that they both represent. In both cases, Christians are taking seriously the centrality of Christ in every facet of what we do. If a holiday compromises our fidelity to Christ, we should be willing to lay it aside. If we can honor our Lord even through the words we choose in greeting one another, we certainly should do so. In all that we do, we should be doing it for the glory of Christ.
Having said this, saying "Merry Christmas" is not inherently virtuous or immoral. Christmas itself is a matter of personal conscience and Christian liberty. Wishing someone else "Merry Christmas" is the same. If you are concerned about the origins of Christmas as a holiday or otherwise don't feel right about saying "Merry Christmas," then don't say it. Strive to maintain a clean conscience before God. If you feel it would compromise your personal stand for Christ to stop saying Merry Christmas, then keep on saying it with boldness! What is important is not the words. What is important is our conscience before God. As we do this, however, it is also vital that we not bludgeon our brother or sister with matters of our own conscience. As Paul wrote to the Romans:
"Who are you to judge the servant of another? To his own master he stands or falls; and he will stand, for the Lord is able to make him stand. One person regards one day above another, another regards every day alike. Each person must be fully convinced in his own mind. He who observes the day, observes it for the Lord, and he who eats, does so for the Lord, for he gives thanks to God; and he who eats not, for the Lord he does not eat, and gives thanks to God," (Romans 14:4-6).
And as he likewise wrote to Timothy:
"But the goal of our instruction is love from a pure heart and a good conscience and a sincere faith. For some men, straying from these things, have turned aside to fruitless discussion," (1 Timothy 1:5-6).
In the matter of saying "Merry Christmas," as in all such matters of holiday celebration, do what you are convinced is right and respect your fellow believers who differ with you. Honor the Lord who was born of a virgin, who died for our sins, and who rose again in victory. Don't fret if the Christian in the pew next to you honors Him differently. If you know a believer who abstains from Christmas for conscience' sake, don't provoke them by wishing them a Merry Christmas. If you yourself abstain from Christmas and a sister wishes you a Merry Christmas anyway, just thank her and say "God bless you" or something else that expresses Christ's love without having to say "Merry Christmas" in return. Differ with one another in love, trust in His grace, and if you celebrate the day, have a Merry Christmas.