Yes, it is common knowledge that Jesus was most likely NOT born on December 25. For a fantastic detailed analysis, here is an outside link that delves deep into it.
Christmas is also not a holiday observance outlined in scripture in any way, shape or form.
However, why not celebrate Jesus’ birthday on the day that is commonly utilized? We have Presidents’ Day on the third Monday in February to commemorate President Washington’s and President Lincoln’s birthdays. That assigned day is not their actual birthdays. We celebrate Thanksgiving on the fourth Thursday of November yet the event that we commonly call the “First Thanksgiving” was celebrated by the Pilgrims after their first harvest in the New World in October 1621.
That being said, as a Jewish follower of Jesus, one who based on the evidence knows that Jesus is the promised Messiah of the Hebrew scriptures, I celebrate Jesus every day. I do not need a set aside day to celebrate Him. I also don’t find the cultural celebration of Christmas to be something I connect with. We light the menorah for Hanukkah. I do display the nativity scene as that speaks the message of the first Christmas, the birth of Jesus. However we do not desire nor put up Christmas trees, Christmas lights, etc. And as a Jewish family, we do not have extended family interested in a family gathering as a Christmas celebration.
BUT, if you do desire to put up a Christmas tree, there is absolutely no reason for you not to! You are not renouncing your Jewish identity, or any other identity. It is simply a tree, something beautiful and seasonal. I do feel that we as Jewish followers of Jesus are in an interesting position, people being more cognizant of the traditions we follow, are we Jewish enough, Christian enough, have we forsaken our roots, changed religions, the analysis goes on and on. It is ridiculous. And sad! And yet, a privilege! Because when leveraged healthfully, it can open the door to some awesome conversations!
So do I ignore the day? No!
Whether attending a Christmas Eve or Christmas Day service, or going into Manhattan with my family and friends to go to Rockefeller Center, or driving around looking at beautiful Christmas displays, or being out of town and enjoying Christmas displays and celebrations there, or whatever else we may find to do, we glorify God and recognize Jesus in all we do.
Christmas is a special, set apart day, and we embrace that, in our private and personal ways. What I do find essential is to ensure that I am doing something. I learned from our very first Christmas as a Jewish family who followed Jesus. We were home, alone, the four of us. Our children were young but old enough to feel the isolation we felt. It was lonely and isolating. Everyone else we knew was with extended family, having their family traditions, many almost sadly boastful about it or oblivious to those who did not have that.
God taught me much in that place of isolation and loneliness! God has given us much and only for the purpose of giving out to others. Not just on the days surrounding holidays, but on the actual day! Since then, always out and about on Christmas. I and we (whoever I am with) always have a great time (and if I would happen to not have anyone to be with on a particular Christmas, I would absolutely be out and about on my own! Being out also provides wonderful opportunities to ever so slightly impact others. Saying Merry Christmas to others we see. Or a smile and a hello in passing. Having some pre paid gift cards to local food stores or fast food chains to hand out to people we pass who are clearly in need. These have become our Christmas traditions and I am grateful to God for how He developed them in me and in us!