mom'sfolly :
The early church made a choice to schedule Christian holidays on the same dates as pagan holidays, as part of the conversion of the masses. It kept familiar rituals and times with what was then a new religion. This is a point of fact.
What we consider a modern American Christmas is cultural, not religious. The Puritans would be appalled, as would many Christians from other cultures, by the way most modern American Christians celebrate Christmas.
The fact of the matter is that historically, every religion has had some sort of holiday that is closely tied to the shortest day of the year. Calendars and traditions change, some things are incorporated in to the what we consider the Christmas tradition are from other sources. That does not make the celebration less significant or less important. Acknowledging the roots of the ritual don't change the underlying faith. For Christians, Christmas is about the birth of Christ, and Easter is about the rebirth of Christ; and the names and traditions have little to do with the faith expressed. Faith is just that, and rejoicing in it, no matter the trappings, is what makes it important, significant and worthy.
If the knowledge that some of the things associated with Christmas don't have Christian origins is enough to shake a person's faith, then they are not steady ground to begin with.
The various celebrations are what the individual believes them to be.