In the name of Allaah, the Benevolent, the Merciful. All praise is due to Allaah, and may peace and blessings be upon the messenger of Allaah, his family, companions, and all those loyal to him. Allaah, the Majestic and High, has indebted us, as part of our worship of Him, with being just and kind to the non-Muslims who are peaceful with the people of Islam. Allaah, the Most High, said: ‘Allaah does not forbid you from being kind and just to those that do not fight you on account of religion nor drive you out from your homes. Indeed, Allaah loves those that are just.’ Part of kindness to them is visiting their sick, sending condolences for their deceased, exchanging gifts to and from, congratulating them for the likes of marriage, a newborn, or upon returning from travel, and the likes of these matters if it is called for via them being your acquaintances, neighbors, relatives, etc. Also, part of kindness is to rush to their aid during a misfortune that befalls them, be it a collective or individual calamity. One of the contemporary scholars even permitted donating blood to their sick and the likes and considered it part of the kindness that Allaah indebted us with, as part of our worshipping Him, in dealing with them.
Additionally, one of the prime portrayals of kindness is advising them with regards to their religion, supplicating for them to be guided, and refraining from any statement or action that would beautify for them their falsehood or cause them to assume the correctness of the religion they are upon. We were commanded (by Allaah), in an expression of our advice and compassion for them, to say: ‘O People of the Book, you are not upon anything until you uphold the Torah, Evangel, and that which was sent down to you from your Lord.’
From here we arrive at the point of inquiry in the question, and say: The default with regards to these religious holidays is that they are part and parcel of these religions and faiths. Therefore, they are to remain exclusively with its people, and it isn’t permissible to share in it based on it being particular to them. Having said that, there is no harm in mentioning general words of congratulations, in the event that there is a clear benefit in doing so, so long as they exclude any infringement upon these particularities. It should not include any sign of approval to the non-Muslim of his religion or acceptance of that. Likewise, it isn’t permissible to bequest a gift to them in the likes of these occasions due to the confusion this causes and it leading them to believe that they are correct in what they are upon. Outside of this context, the opportunity for gift-exchange remains available throughout the year because the harm isn’t in the concept of gifting, but rather in its timing and connecting it with this occasion. The only exception to this would be if this occasion had been divorced from its religious roots and became a solely social occasion. In this case, the matter would return back to the default principle, and that is the permissibility of exchanging gifts if it is called for via them being your acquaintances, neighbors, relatives, your hoping of softening their hearts towards Islam, and similar virtuous aims.
This impermissibility is even clearer with regards to the Islamic centers since they are the exemplars and role models; the religious values are exported from them, and they are the ones that are imitated by others.
As for accepting their gifts, there is no harm in that because of what was narrated that Ali, may Allaah be pleased with him, accepted them. Also, it was reported that a woman asked A’ishah, may Allaah be pleased with her, and said: ‘We have food from the fire-worshippers. It is from their holidays, and they give us from it as gifts.’ A’ishah responded: ‘As for what was slaughtered for that day, do not eat, but eat from their trees.’ – meaning: Do not eat from what was slaughtered for other than Allaah for their holidays, nor that which was slaughtered for the festive occasion of that day, but eat the other things such as fruits and sweets. And Allaah, the Most High, knows best.