I think we need a new term for these type of issues, for now I will just call them "asshole issues". Let me explain myself. These are just greetings, most people don't really see either one as having much significance behind them. They are just being friendly. Also I would bet my life that if most people were told by the person receiving party that they don't celebrate Christmas they wouldn't care and just wish them whatever.
This is an "asshole issue" because if you honestly believe this is an issue you are being an asshole. Again I would bet my life that a vast majority of people by saying either one is not trying to push any type of preference onto you, religious or otherwise. People say Merry Christmas because it is a major holiday celebrated by a large segment of the population. People say Happy Holidays because in addition to Christmas, Hanukkah, and Kwanza there is New Year's. Obviously people are going make assumptions but I am positive if asked a vast majority will be happy to response accordingly. When you are trying to turn people being friendly to one another into some culture war you are just an asshole.