Do you have a problem with people saying "Merry Christmas"?

I don't. I don't mind if Christians tell me Merry Christmas or Jews say Happy Hanukkah. First Amendment protects peoples' rights to say these things. I don't have a problem with religious icons or Christmas music either. People have the right to share these things, as long as they aren't preaching. Saying Merry Christmas isn't preaching, it's sharing your views. The other person has every right to say Happy Holidays back if they don't agree.