Far from being a way of leaving the "Christ" out of "Christmas", this abbreviation has been in use by Christians for at least hundreds of years!
The history of shortening "Christmas" to "Xmas" is similar to how the "Jesus fish" is a meaningful symbol that early Christians used to identify each other: The "X" in question is really the Greek letter Chi, which looks like the English letter "X". The Ancient Greek word Χριστός was translated to English as "Christ" - it's that first Greek letter that is really the origin of the X in Xmas.
Newer interpretations where people think Xmas somehow diminishes the Christian meaning of Christmas are ignoring the true history of how the "X" was used and what it represents.
Learn more by reading the very well-written The Origin of "Xmas" at the Christian Resource Institute and the Wikipedia entry for Xmas.
(Image via Tobi Firestone on Flickr)