Praise be to Allaah.
Greeting the kuffaar on Christmas and other religious holidays of theirs is haraam, by consensus, as Ibn al-Qayyim, may Allaah have mercy on him, said in Ahkaam Ahl al-Dhimmah: “Congratulating the kuffaar on the rituals that belong only to them is haraam by consensus, as is congratulating them on their festivals and fasts by saying ‘A happy festival to you’ or ‘May you enjoy your festival,’ and so on. If the one who says this has been saved from kufr, it is still forbidden. It is like congratulating someone for prostrating to the cross, or even worse than that. It is as great a sin as congratulating someone for drinking wine, or murdering someone, or having illicit sexual relations, and so on. Many of those who have no respect for their religion fall into this error; they do not realize the offensiveness of their actions. Whoever congratulates a person for his disobedience or bid’ah or kufr exposes himself to the wrath and anger of Allaah.”