Is it okay for a Christian to celebrate a holiday that has pagan roots? Yes.
We can see a very similar principle in Romans 14 as well as Colossians 2. Paul was dealing with a church that was divided along the lines of those who came out of Judaism and those who had a Pagan background. Those with a Jewish background tended to be more “legalistic” (literally, wanting to follow the Old Covenant law), whereas the Gentiles (and Hellenistic Jews) didn’t really have that much of a hangup. The more conservative Jews were quick to say “do not touch, do not eat, do not drink” those things that were not sanctified.
This issue(s) came to a head because the church would eat together and then some of the more “liberally minded” Christians were bringing meat and wine that had been used in pagan temples or part of pagan worship practices. It was cheaper. This appalled the more strict Jews.
What was Paul’s response? Essentially, he said “keep it to yourself.” Here’s the summary. We are free in Christ to worship however we feel impressed by the Holy Spirit. There are not specific “holy days” and there are not specific “holy ways” to worship. It’s a matter of conscience. Idols are nothing, so it doesn’t matter if something you can benefit from was used previously in pagan worship, if it helps you, go for it, there’s nothing wrong with it!
However, there are some people who have a weaker faith who don’t yet live in that freedom. As a matter of personal conscience, they just can’t bring them to eat meat sacrificed to idols or drink wine used in pagan worship. They have a personal problem with it, so others with a better understanding of their freedom in the New Covenant need to still be sensitive to their brothers and sisters in Christ who aren’t quite there yet.
Those who are more mature need to defer to those who are less mature and think that appropriation of formerly pagan things can somehow hamper their faith.
So what does this say about Christmas? No, there’s no command to observe Christmas in the Bible… yet there was no Hanukkah in the Bible in Jesus’ time either, and yet he still celebrated that secular national holiday (see John 10:22-23). Why would we want to discourage people from celebrating the birth of our Savior?! I sure don’t. But, some do. So it’s fine to state your own convictions, but we also need to be sensitive to those who are under conviction.
Now… to those who would say “Christians should not celebrate Christmas” I would say that you are going too far. You are putting words in God’s mouth that you should not. Just as Paul encouraged the church in the first century, he encourages us as well, keep your convictions to yourself. Don’t hold other Christians to YOUR standards, hold them to God’s standards (i.e. “judge rightly”). And, I’d also say, have a Merry Christmas 🙂