Even if we are Muslim, it's nothing wrong to greet Christian brothers and sisters "Merry Christmas." Because it's their festival and we are not to judge other that they are right or wrong. Allah will do, not us. If we get Eid Mubarak greeting from other non-muslim, we would be happy because you are showing your affection, care, hospitality gestures to other. We should not take everything so seriously and rigid. Just take it easy. You can have different opinion.
