Is Giving Udhiyah Meat to Non-Muslims Permissible?
Question

Is it permissible to give meat from the udhiyah to our non-Muslim neighbours? I hope you can answer my question in accordance with the Quran and Sunnah, along with the evidence. I have a Christian colleague who refuses to accept the udhiyah meat from me, and he says that is because the Bible that they have does not allow them to do that.
Praise be to Allah.There is nothing wrong with giving meat from the udhiyah to a non-Muslim , especially if he is a relative or neighbour or is poor. 
That is indicated by the verse in which Allah, may He be exalted, says (interpretation of the meaning):
“Allah does not forbid you to deal justly and kindly with those who fought not against you on account of religion and did not drive you out of your homes. Verily, Allah loves those who deal with equity.” [al-Mumtahinah 60:8] 
Giving him some meat from the udhiyah comes under the heading of dealing justly and kindly with them, which Allah has permitted to us.
Mujahid narrated that a sheep was slaughtered for ‘Abdullah ibn ‘Amr by a member of his family, and when he came, he said: Did you give some to our Jewish neighbour, did you give some to our Jewish neighbour? For I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “Jibril kept urging me to treat neighbours kindly until I thought that he would make neighbours heirs.” (Narrated by at-Tirmidhi (1943); classed as sahih by al-Albani) 
Ibn Qudamah said: 
“It is permissible to give some of it to a disbeliever, because it is voluntary charity which may be given to non-Muslims living under Muslim rule and prisoners of war, like all other kinds of voluntary charity.” (Al-Mughni, 9/450) 
In Fatawa al-Lajnah ad-Daimah (11/424) it says:
“It is permissible for us to give meat from the udhiyah to non-Muslims who have a treaty with the Muslims and to prisoners of war, and it is permissible to give it to him on the basis that he is poor, or a relative, or a neighbour, or so as to soften his heart towards Islam, because of the general meaning of the verses in which Allah, may He be exalted, says (interpretation of the meaning):
“Allah does not forbid you to deal justly and kindly with those who fought not against you on account of religion and did not drive you out of your homes. Verily, Allah loves those who deal with equity.” [al-Mumtahinah 60:8].
And because the Prophet (blessings and peace of Allah be upon him) instructed Asma bint Abi Bakr (may Allah be pleased with her) to uphold ties of kinship with her mother by giving her money when she was still a mushrik at the time of the truce.”
Shaykh Ibn Baz (may Allah have mercy on him) said: 
“With regard to the disbeliever who is not in a state of war with us, such as one who has been granted protection by the Muslims or one who is living under Muslim rule, he may be given meat from the udhiyah, and other kinds of charity.” (Majmu‘ Fatawa Ibn Baz, 18/48) 
For more about udhiyah, please see these answers: 36432 , 36755 , 36651 , and 36663  
And Allah knows best.