Christmas is not actually the "birthday" of God or Jesus Christ. That is not what the feast or solemnity is on the calendar of the church or Christianity.
As Heidi Russell, Loyola University professor explained in teaching litrugical theology:
Christmas is the feast of the incarnation. In Christmas we do celebrate the nativity or birth of Christ, but what we are celebrating is not simply Jesus’ “birthday,” the way we celebrate our own birthdays. We are celebrating the mystery of Emmanuel, God-with-us, God revealed in time and space....St. Athanasius, one of the great fathers and theologians of the Church, tells us: "The Son of God became human so that we might become God." Obviously we do not become God in the way that God is God, but we become God-like, we are divinized...We partake in the divine nature. St. Irenaeus puts it another way: "For this is why the Word became man, and the Son of God became the Son of man: so that man, by entering into communion with the Word and thus receiving divine sonship, might become a son of God."
It is centered around the theology of Isaiah 7:14, Matthew 1:23 and 2 Peter 1:4 where the texts tell us that God comes to be with us and we become partakers of the divine nature.
The early church did not teach the Jesus was born on this date necessarily. And it is not celebrated as a 24-hour day (except perhaps by Fundamentalists). Even by Protestants the date is observed as Roman Catholics and Greek Orthodox Christians do, for 8 days, beginning at sundown on the 24th of December until sundown on January 1st.
A birthday does not last 8 days. An octave is a liturgical observance based on Jewish festivals which included a week surrounded by two Sabbaths, one on each end, like Passover which begins with a Sabbath, has six days in between, and then ends with another Sabbath.
In Christianity, birthdays are not celebrated. Instead martyrs and saints are given memorials, usually on the day of their death or burial because that is considered the day they enter their eternal reward in Heaven. There are no birthdays on the Christian calendar, including for Jesus of Nazareth.
Interestingly, his death is celebrated. It is called "Good Friday."
Christianity uses the Divine Office (the Liturgy of the Hours) or the Book of Common Prayer to count the days of the year, placing holy days like Easter and Christmas, etc. in their place, including many memorials of saints. For Christmas the first day is considered a Christian Sabbath, which requires that all Christians attend Church services, and the 8th day, January 1st is also a holy day of obligation, another Christian Sabbath, regardless of what day of the week either day these land on.
I would say it is no more hypocritical for an atheist to play with cultural holiday traditions anymore than it is for people who claim to be Christian to not know how the Nativity of the Lord is actually observed--and that it is not really a "birthday."