In America it's politically correct to say "Happy Holidays" from late November through December because people of so many cultures and religious backgrounds live here. I'm not a Christian myself but I don't mind hearing "Merry Christmas," nor do I worry much about getting the greeting right as long as people are of good cheer. Greeting each other kindly and wishing each other goodness is what's important.
This is the day we mark on our calendars to commemorate the birth of someone who has had a monumental influence on our culture, regardless of whether or not you believe he existed. If we did as he asked us to do, this Earth would be a peaceful place indeed. I think he'd want us to greet each other kindly and wish each other goodness.
Goodwill starts in our hearts. From there, it can go everywhere. So Merry Christmas, whatever you celebrate.