NOTE: It should be noted that the below answer is the English translation of the Fatwa issued by Jamia Uloom Islamia Allama Yusuf Banuri Town, Karachi, Pakistan.
What is the ruling on greeting a non-Muslim at Christmas? Is this shirk?
The Shari’ah ruling on greeting non-Muslims on the occasion of religious festivals is that since these festivals are based on polytheistic beliefs, and as Muslims, it is necessary for us to express our dissociation and detachment from polytheism. Greeting them on Christmas shows support and acceptance of their point of view. So it is not permissible to wish them Merry Christmas.
If this greeting is meant to honor their religion, then there is a danger of disbelief. And if someone explicitly speaks anything related to polytheism at Christmas, then there is no doubt about his shirk.