Here is what Fred Lindemann thought about not offering Holy Communion on either Christmas Eve or Christmas Day 60 years ago:

Some churches have eliminated the Holy Communion entirely on Christmas (Eve and) Day. The reason is said to be that the members and children and visitors attend in unusual numbers and that the visiting nonmembers do not wish to sit idly in the pews while the members communicate. For the sake of people who attend once or twice during the year God’s saints are deprived of the Holy Sacrament! A far simpler solution would be to arrange a special program for all who even at Christmas are in a hurry. In such a special service the choirs may sing to their hearts’ content, the organist play interminable, the pastor limit his ministry to a brief reading and a short prayer. A ceremony of candle lighting may be performed. In fact, any and every sentimental prettiness observed in churches that have no Holy Sacrament may be imitated. This should satisfy the nonchurched and induce them to come again on Easter. But the Services appointed by the Church, The Communion with its own set of Propers, is chiefly for the faithful. The Feast of the Holy Nativity is not an occasion to deprive the faithful of the Holy Communion for the sake of the infrequent visitor.. .. Christmas, the Mass of Christ’s Day, is incomplete without he Eucharist.

Fred H. Lindemann, The Sermon and the Propers, vol 1 The Advent and Epiphany Seasons (St. Louis: Concordia Publishing House, 1958) 68.