What can and What cannot be eating from the Non-Muslims Food in and outside their Festival Periods
Praise be to Allah
First of all, there's no ikhtilaaf (difference of opinion) in the rulings regarding Muslims eating the food of the People of the Scripture. If it is food prepared outside their festivity, it is permissible to accept it so as to soften their hearts and make Islam attractive to them, as the Prophet (peace and blessings of Allaah be upon him) accepted gifts from some of the kaafirs. But if the food is that which is shared on the day of their festival, we say if it is;

1. GIFT: With regard to accepting a gift from a kaafir on the day of his festival, there is nothing wrong with that, so far it is something that is not used in perpetrating or participating in it or approving of it, rather it should be accepted as an act of kindness, with the aim of softening his heart and calling him to Islam. Allaah has permitted kindness and fair treatment towards the kaafir who is not fighting the Muslims, as He says (interpretation of the meaning): “Allaah does not forbid you to deal justly and kindly with those who fought not against you on account of religion nor drove you out of your homes. Verily, Allaah loves those who deal with equity” [al-Mumtahanah 60:8]

But kindness and fair treatment does not mean friendship and love, because it is not permitted to take a kaafir as a friend or love him. Please take the pleasure of checking the following verses of the Qur’an: al-Mujaadilah (Q58: vs22), al-Mumtahanah (Q60: vs 1), Aal ‘Imraan (Q3: vs118), and many other verses which speaks affirmative of it.

Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said: As for accepting a gift from them on the day of their festival, we have quoted above that ‘Ali ibn Abi Taalib was brought a gift on the occasion of Nayrooz and he accepted it.

Ibn Abi Shaybah narrated that a woman asked ‘Aa’ishah: We have some wet nurses from among the Magians, and they have a festival on which they bring us gifts. She said: As for what is slaughtered for that day, do not eat it, but eat from their vegetables.

All of these indicates that the festival does not make it forbidden to accept their gifts, rather the ruling is the same whether it is their festival or not, because that does not involve helping them with the symbols of their kufr (disbelief).

2. Other Than a Gift: It is only permissible to eat of the food of the people of the Book, during their festivals that which has not been slaughtered for the festival (which means anything slaughtered for the festival, should be done away with), whether it is bought or received as a gift. As for meat slaughtered by the Mushrikun, the ruling on that is well known, and it is haraam (forbidden) according to all. As for that which is slaughtered by the people of the Book for their festivals and that which they slaughter as an act of worship to draw close to anything other than Allaah (just as the Muslims offer sacrifices as an act of worship to draw closer to Allaah as well), namely as that which they sacrifice to the Messiah (Jesus), two views have been narrated from Ahmad concerning that, the most well known of which in his texts is that, it is not permissible to eat it even if the name of something other than Allaah has not been mentioned over it. The prohibition on that was narrated from ‘Aa’ishah and ‘Abd-Allaah ibn ‘Umar … End quote from Iqtida’ al-Siraat al-Mustaqeem (1/251). [Those bold characters indicates that even if they call you as a Muslim to come and slaughter the meat for them since they know we don't eat meat that names other than Allaah was mentioned on, it is still not permissible to eat from it because the intention is sacrificing for what Allaah has not ordained]
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Conclusion: It is permissible for you to accept the gift from your Christian neighbour on the day of their festival, subject to the following conditions:
1 – This gift should not be meat that has been slaughtered for the festival.
2 – It should not be something that may be used to help in imitating them on the day of their festival.
3 – You should explain to your children the belief in al-wala’ wa’l-bara’ (loyalty and friendship vs. disavowal and enmity), lest a love of this festival or a fondness for the giver be instilled in their hearts.
4 – The gift should be accepted with the aim of softening their heart and calling her to Islam, not with friendship and love.

Note: If the gift is something that it is not permissible to accept, then the refusal to accept it should be accompanied by an explanation of why it is being refused, such as saying, “We only refused your gift because it is meat that was slaughtered for the festival, and it is not permissible for us to eat it, or these things are only accepted by those who are taking part in the celebrations, and we do not celebrate this festival, because it is not part of our religion, and it involves beliefs that we do not believe in” and so on, which is a starting point for calling them to Islam and explaining the danger of the kufr that they follow.

The Muslim should be proud of his religion and apply its rulings, and he should not give them up out of shyness or to impress anyone, for Allaah is more deserving of us feeling shy before Him. And Allaah Knows Best!