Muslims have two festivals: Eid al-Fitr and Eid al-Adha. Most scholars say that Muslims should not take part in the religious rites of other faiths, and they differ on whether it is allowed to greet neighbours on their holidays or to attend a celebration as a guest.
The fuller answer
Muslims honour Jesus and so many of them respect the Christmas season, but they do not believe he is God's son, which is the basis of the celebration. Some scholars say that greeting Christians on their holiday is part of the kindness and justice that the Quran commands, and others advise against it. Almost all agree that it is fine to be kind, to accept a gift and to be a good neighbour.
If a Muslim friend declines to take part in a celebration, it is out of religious conviction and not unfriendliness. Many Muslims join workplace events or visits for the sake of friendship while avoiding the religious part.
Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly.
This answer follows the mainstream Sunni understanding and is general learning, not a fatwa. Where Muslims differ, the answer says so. Have a question of your own? Write to us.