Christmas is first a Christian holy day: the Nativity. In this country it is also a public fact of the civic year — a federal holiday, a quiet Main Street, a church that does not need a permit to sing.
That is not a state church. It is the First Amendment working as designed: Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof. People may worship, or not. They may keep December 25 as the birth of Christ, as a family table, or as a day of rest. The government does not assign the meaning. The people do.
A free country can say Merry Christmas in the open. The greatness is not that every American believes the same thing. It is that no official gets to forbid the belief — or the feast.