Praise be to Allah.
What the Shi’ah do on ‘Ashoora’ of slapping their cheeks, striking and cutting their heads, shedding their blood and making special foods, is all bid’ah and reprehensible innovation, as has been explained in the answer to question no. 4033 and 9438. It is not permissible to take part in that, or to help those who do it, because that is cooperating in sin and transgression.
And it is not permissible to eat this food that they have prepared for their innovation and misguidance.
Shaykh Ibn Baaz (may Allaah have mercy on him) said: This is an abhorrent evil and reprehensible innovation which must be abandoned; it is not permissible to take part in it and it is not permissible to eat the food that is offered.
And he said: It is not permissible take part in it or to eat of these meats or drink these drinks [prepared for this occasion]. If the meat has been slaughtered for anyone other than Allaah, among Ahl al-Bayt [the Prophet’s family] or anyone else, then it is major shirk, because Allaah, may He be glorified and exalted, says (interpretation of the meaning):
“. Say (O Muhammad صلى الله عليه وسلم): ‘Verily, my Salaah (prayer), my sacrifice, my living, and my dying are for Allaah, the Lord of the ‘Aalameen (mankind, jinn and all that exists).
163. ‘He has no partner. And of this I have been commanded, and I am the first of the Muslims’”
“Verily, We have granted you (O Muhammad صلى الله عليه وسلم) Al‑Kawthar (a river in Paradise).
2. Therefore turn in prayer to your Lord and sacrifice (to Him only)”
End quote from Fataawa al-Shaykh ‘Abd al-‘Azeez ibn Baaz (8/320).
But if your refusing to accept their food will pose a danger to you, then there is nothing wrong with accepting it so as to ward off harm.
And Allaah knows best.