I love how we justify celebrating something founded on pagan roots by saying we already participate in things with pagan roots. With that logic, we can "Christianize" anything.
I believe we can, but not that we necessarily should. God is mightier than the world, but we can't undo history.
Do we stop eating fruit, because the eating of the forbidden fruit was the original sin? Do we stop learning other languages, because God imposed languages as a control after man's attempted rebellion at Babel? Did Paul in Athens (Acts 17) distance himself from the pagan "Unknown God"? Rather, he used this as an opportunity to preach the One True God to the pagans.
I'm sure for everything we might do, there are probably some pagans who lived before that did something similar. My point was if we stop doing all the things that have some tentative link to paganism, we wouldn't be able to do anything. We are called to be in the world, but not of the world. Rejecting anything with a potential link to paganism is likely not possible in this life.
Even some of the non-pagan things in scripture - e.g. circumcision - are spoken against for Christians in the New Testament. This isn't to say such things are bad - but what is important is the reason for why they were done. Circumcision was condemned for the Galatians because they were adding this to the gospel and thereby invalidating the Good News of Salvation - not because circumcision is inherently evil, as Paul even circumcised Timothy to assist in his preaching to the Jews.
In my view, for Western Christians to totally divorce themselves from Christmas cancels out one of the best witness opportunities of the culture. To my thinking, it is also hypocritical, if these Christians then do not also divorce themselves from all other hints of paganism in the culture, such as the use of the days of the week, the names of the planets, and even the calendar. The only logically consistent choices in my mind are accepting that we live in the world (but for us to not be of the world, and do all for the glory of God), or adopting the lifestyle of an early century monk.
1 Corinthians 10:23 - 33
23 All things are lawful for me, but all things are not expedient: all things are lawful for me, but all things edify not.
24 Let no man seek his own, but every man another's wealth.
25 Whatsoever is sold in the shambles, that eat, asking no question for conscience sake:
26 For the earth is the Lord's, and the fulness thereof.
27 If any of them that believe not bid you to a feast, and ye be disposed to go; whatsoever is set before you, eat, asking no question for conscience sake.
28 But if any man say unto you, This is offered in sacrifice unto idols, eat not for his sake that shewed it, and for conscience sake: for the earth is the Lord's, and the fulness thereof:
29 Conscience, I say, not thine own, but of the other: for why is my liberty judged of another man's conscience?
30 For if I by grace be a partaker, why am I evil spoken of for that for which I give thanks?
31 Whether therefore ye eat, or drink, or whatsoever ye do, do all to the glory of God.
32 Give none offence, neither to the Jews, nor to the Gentiles, nor to the church of God:
33 Even as I please all men in all things, not seeking mine own profit, but the profit of many, that they may be saved