Christmas traditions that have pagan origins are the Christmas Tree; the celebration of Christmas in Winter (by the winter solstice); the Yule log; the giving of gifts; and I am sure there are more, but we will just deal with these for now.
The Christmas Tree, Yule log, and the winter solstice, are definitely related to the pagan traditions, but why did the Christian Church adopt them? When humanity was mired in the dark or middle ages, and pagans were converting to Christianity, they were used to celebrating and using these symbols to celebrate the winter solstice. Old habits die hard, and the Christians now found themselves in a quandry about what to do with this time of year. The Christian Church had already adopted the date of 25 December to celebrate Christmas, so that was not a problem, but how to get rid of the old pagan rituals? So the Christian Church changed the rituals into Christian rituals, by associating them with Christian ideas, concepts and Scripture.
For Example, the Christmas tree has a double meaning, both the evergreen, showing that Jesus brings eternal life, and as a forewarning of the Cross. For it was wood upon which He was crucified (in many places, the Scriptures prophesy "a tree").
Now, some people say we should not use a tree, as the pagans used one before Christians did for their rituals and celebrations. But what do the Scriptures say?
In Romans, 14 --
5 One man considers one day more sacred than another; another man considers every day alike. Each one should be fully convinced in his own mind. 6 He who regards one day as special, does so to the Lord. He who eats meat, eats to the Lord, for he gives thanks to God; and he who abstains, does so to the Lord and gives thanks to God. 7 For none of us lives to himself alone and none of us dies to himself alone. 8 If we live, we live to the Lord; and if we die, we die to the Lord. So, whether we live or die, we belong to the Lord. The Holy Bible : New International Version. electronic ed. Grand Rapids : Zondervan, 1996, c1984, S. Ro 14:5-8
This does not apply only to the celebration of a particular day, but if you take this passage (as one must always do) within the context of the chapter, and book, and indeed the entire Bible, you will see that the concept is that we should allow grace to others who believe slightly differently than ourselves. (However this does not mean all teachings, or beliefs are acceptable -- There are limits to orthodoxy.)
Most importantly, the Scriptures tell us to do all things for the Glory of God in Christ Jesus, and to do all things in LOVE. So, just because I do something, or do not do something, does not mean it is right, or wrong for someone else to do it. It depends on their faith journey with their Creator, and Redeemer, Jesus Christ. (see above Scripture again)
Let us all be tolerant of those who disagree with us, and give as much grace to them, as we would like to receive from them!