For a long title, a short post.
Basically it goes back to the earlier post about moving Christmas. Christmas is actually a bastardized version of two celebrations, the birth of Christ for the Christians, and the Unconquered Sun celebration for the pagans. Here is a short history of Unconquered Sun and why the birth of christ was actually moved from Jan 6th to Dec 25th.
And the Yule Log has nothing to do with Christianity.
So if you don't put up a nativity, and you don't sing the religous x-mas carols, you can celebrate Christmas and divorce the christian references all together. I find that interesting and oddly comforting.