Honestly, with how most people act in today's society, I'd think a stranger, no matter what they celebrate, should be happy to receive any sort of well wishes at all. If I say Merry Christmas to you, it means more to me than if I say Happy Holidays. Merry Christmas is saying I want you to have a joyous and happy time of the advent season, which revolves around the Christmas holiday.
Fun fact: Christmas is also, and has been for a long time, a pagan holiday. It's just so caught up in Christianity celebrating the birth of Jesus on it (which didn't really happen on any December 25 of our modern calendar) that we forget that.
If you get offended when I wish you a Merry Christmas... Let's just say I may end up wishing something else on you
Post-scriptum note: "you" is referring to a generalized, non-specific third person non-party to this conversation/debate that is in no way shape or form supposed to resemble a real life or fictional person, place, event, scene, or action from any other location. (did I cover all my legal butts there?)