Living in harmony does not mean everyone gets his own way, or that we should have to change our oldest customs to avoid offending someone who came from another country.
It means living with others' customs and accepting them. (If we went to some of the countries where our immigrants come from, what do you think would happen if we insisted they change their customs and adopt ours?)
Who cares about the actual date of Jesus Christ's birth? Christians have celebrated it on Dec. 25 for hundreds of years. Ergo, Merry Christmas is the proper term of greeting. "Season's greetings" or "happy holidays" are meaningless. We are not celebrating winter, the solstice, or the fact that we can have a few days off from work.
So, rather than be offended, people who celebrate it in a different manner, and who use a different greeting, should observe their customs and not be offended by ours. Behaving rationally dictates that if one says "merry Christmas" to someone, and the other answers with their own ethnic or religious greeting, neither should feel offended.