That would make sense for them to wish YOU a Merry Christmas if they knew you were a Christian.
and even if I or they are not, we can share the sentiment of the season.
The sentiment of the season is "I hope you have a nice holiday celebration of the birth of the Lord and savior of the world, Jesus Christ, God's only son, who came to earth as a gift from God, to reconcile sinners to himself so that we might all be saved from otherwise certain eternal death".
THAT is the sentiment. Why on earth would you wish a Muslim or Jew or pagan or atheist such a greeting? Makes no sense at all.
"Why on earth would you wish a Muslim or Jew or pagan or atheist such a greeting? Makes no sense at all."
Because that way they know that you wish them well, and hope for them to gain blessings? Peace on Earth, good will to men, all that stuff?