The simple answer to your question is that 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.
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.