Did the Messenger (peace and blessings be upon him) greet Jews and Christians for their holidays or participate in their celebrations?

It has not been reported that the Messenger of Allah, peace and blessings be upon him, participated with Jews, Christians, or other disbelievers in their festivals. Rather, he forbade persistence in celebrating pre-Islamic festivals, for Allah replaced them for Muslims with the two days of Eid al-Adha and Eid al-Fitr. Some of the early Muslims interpreted "falsehood" (al-zoor) in the verse: "And those who do not bear witness to falsehood" (Quran 25:72) as referring to the festivals of the disbelievers. Indeed, there is a prohibition against participating with disbelievers in their festivals.