It feels good to be clever and edgy, so everywhere people can be found who pleasure themselves by pointing out that Christmas is not really “Christian” or that the celebration of the Prophet Muhammad’s birthday was not done by early Muslims so it is not really “Islamic” and so on and so forth.
The fact that Christmas shares much of its symbology with pre-Christian religions does not in any way take away from it is Christianness. All of these symbols can be thought of as remnants of religions that were originally religions of some of God’s prophets that were changed over time, or as celebrations of natural human desires for growth, rebirth, renewal and light. There is absolutely nothing wrong with merging all of these symbols together and giving it a Christian meaning. What matters is whether Christians find in such symbols meaning and satisfaction.
Prophet Muhammad and his earliest followers had probably never seen a dome in their lives, yet today domes are a central feature of Islamic architecture. Feel free to keep pointing out that domes were originally taken from non-Muslim Persians, the point remains is that today Muslims find domes pretty, familiar and useful parts of their culture, therefore they are Islamic. In the same way, if Christians today find the Christmas tree and related items pretty, familiar and useful parts of their culture, then these are very much Christian. Saying they are not Christian is like saying that the paper the Bible is printed on is “secular”, or that the alphabet they use was taken from pagan Romans, therefore we should make fun of Christians for reading a book printed on secular paper in pagan Roman letters.
If it feels meaningfully Christian to Christians, then it is Christian.