It depends on how you keep it. But the word Christ means Jesus the Messiah and mass is a liturgical service in Christianity.
Mass is the main eucharistic liturgical service in many forms of Western Christianity.
Mass (liturgy) - Wikipedia
So, the word Christmas is in no way pagan. But maybe some have pagan habits mixed to Christmas. That doesn’t mean Christmas is pagan, it just means some have mixed pagan things to Christmas.
Can you show me where Christianity was ever said to be “liturgical’? There was never any ritual or repetition advocated for Christians, the majority of whom would not be Jewish and therefore not obligated to perform Jewish observances or to follow their formalities. Gentiles had very few obligations placed on them. (Acts 15:14; Acts 15:28-29) Education about God and his Christ was more important than empty ritual performance. (John 17:3)
The “New Covenant” introduced the proper way for Christians to worship the Father....not the son.
Like the Pope, Mass is entirely Catholic, not Christian. I don’t believe that there is even a resemblance between Catholicism and what Jesus began.
I believe that to celebrate pagan festivals under a thin “Christian” label is not only dishonest, it is a direct violation of Christian teaching, and therefore dishonouring the God they claim to worship. If you read 2 Corinthians 6:14-18 you will see that true Christians are told not to “touch” what is “unclean” in God’s eyes. There can be no “sharing” with them. How often did God punish his own people for their excursions into false worship? He hates it! Jeremiah called it spiritual “adultery”. (Jeremiah 3:8-9)
How many people know that the Roman Catholic Church was instituted for political reasons, not because the Roman Emperor was a Christian? As an astute politician, he instituted a “universal” (Catholic) religion to consolidate his divided empire. He incorporated elements of both so as to keep everyone happy. From my studies, what he introduced was never “Christian” from its inception. What does Jesus say to those who call him “Lord on the day of judgment? “I never knew you”.....what does the word “never” mean? (Matthew 7:21-23)