We live in a country where there are many Bid'ahs in the month of Muharram and my neighbors cook food on these days, especially on the days of the memory of the death of Al-Husayn ibn ‘Ali, may Allaah be pleased with him, and give it to us. They make this every year. Is it permissible to eat this food? If not, should we throw it?
May Allaah guide you.

All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

Celebrating the anniversaries of the dead, whether the dead person is Al-Hasan ibn ‘Ali, or any other person, is a Bid‘ah that the Muslim should avoid and should not participate in. You should advise those who do this Bid‘ah and guide them to follow the Sunnah of the Prophet, sallallaahu ‘alayhi wa sallam. If benefit lies in accepting a gift on this ocassion, then it is alright to accept it as scholars said that it is permissible to accept the gifts of the disbelievers on their festivals, so the gift of Muslims who do a particular bid‘ah is worthier of being accepted.

Conversely, if the benefit lies in refusing this gift so that people would be dettered and would not do such Bid‘ahs, then you should not accept it. You should reject it in a gentle manner and show that you returned it only because it is related to a Bid‘ah and that you are keen on putting an end to this Bid‘ah. 

Allaah Knows best.