The X in Christmas is used like the R in R.C. My given name at birth was Robert Charles, although before I was even taken home from the hospital my parents called me by my initials, R.C., and nobody seems to be too scandalized by that.
X can mean so many things. For example, when we want to denote an unknown quantity, we use the symbol X. It can refer to an obscene level of films, something that is X-rated. People seem to express chagrin about seeing Christ's name dropped and replaced by this symbol for an unknown quantity X. Every year you see the signs and the bumper stickers saying, "Put Christ back into Christmas" as a response to this substitution of the letter X for the name of Christ.
There's no X in Christmas
First of all, you have to understand that it is not the letter X that is put into Christmas. We see the English letter X there, but actually what it involves is the first letter of the Greek name for Christ. Christos is the New Testament Greek for Christ. The first letter of the Greek word Christos is transliterated into our alphabet as an X. That X has come through church history to be a shorthand symbol for the name of Christ.
There's a long and sacred history of the use of X to symbolize the name of Christ, and from its origin, it has meant no disrespect
We don't see people protesting the use of the Greek letter theta, which is an O with a line across the middle. We use that as a shorthand abbreviation for God because it is the first letter of the word Theos, the Greek word for God.
X has a long and sacred history
The idea of X as an abbreviation for the name of Christ came into use in our culture with no intent to show any disrespect for Jesus. The church has used the symbol of the fish historically because it is an acronym. Fish in Greek (ichthus) involved the use of the first letters for the Greek phrase "Jesus Christ, Son of God, Savior." So the early Christians would take the first letter of those words and put those letters together to spell the Greek word for fish. That's how the symbol of the fish became the universal symbol of Christendom. There's a long and sacred history of the use of X to symbolize the name of Christ, and from its origin, it has meant no disrespect.
Adapted from Now, That’s a Good Question! ©1996 by R.C. Sproul. Used by permission of Tyndale.