Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
There is nothing wrong with attending the funerals of non-Muslim relatives as it is a social and ethical duty that we owe each other.
Answering your question, Sheikh Kifah Mustapha, the Imam and Director of The Prayer Center of Orland Park and representative for Dar El Fatwa of Lebanon in the US, states:
Islam honors humans
Allah the Almighty honors humans. Allah said: {And We have certainly honored the children of Adam.} (Al-Israa 17:70)
It is the duty of human to honor the death of another human being as the Quran tells us in the story of the two sons of Adam. Allah said:
{Then Allah sent a crow searching in the ground to show him how to hide the disgrace of his brother. He said, “O woe to me! Have I failed to be like this crow and hide the body of my brother?” And he became of the regretful.} (Al-Maidah 5:31)
The human experience upon loss of loved ones is mourning and grief regardless of their faith. Prophet Mohammad (peace be upon him) cried upon the death of his son Ibrahim and other dear ones to his heart.
And for that people should condole each other in such moments of loss and grief.
In Islam, this is an honorable thing as we were told by Prophet Muhammad: “the rights of a Muslim are five; returning Salam, visiting in case of illness, attending funeral, Dua upon sneezing and answering invitations.” (Al-Bukhari)
Attending funerals of non-Muslims
This honor is not limited to Muslims only as we know that a funeral passed by Prophet Muhammad and he stood for it in honor. The Companions said: “It is for a Jewish person! Prophet Muhammad said: “if you see a funeral stand up?” (Al-Bukhari) And in another narration: “Isn’t it a soul!” (Al-Bukhari)
When the uncle of Prophet Muhammad, Abu Talib, died, the Prophet told his son Imam Ali (may Allah be pleased with him): “Go and burry him.” Ali said: he died as a non-believer! The Prophet said: “Go and burry him.” When Ali came back, the Prophet said: “Go take a shower.” (Abu Dawud and An-Nasai)
By default, burying a person would include giving him a bath, covering him with shrouds and walking with funeral and digging a grave and lowering him to earth.
Abu Wael, one of the Prophet’s Companions, said: My mother died and she was Christian and I asked Umar and he said: ride your camel and walk ahead of the funeral. (Ibn Abi Shaibah and Ibn Hazm)
Allah bestowed a general blanket of ethics for humans when dealing with each other regardless of their differences in religion. Allah said: {Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes – from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly.} (Al-Mumtahanah 60:8)
Allah used the term (Al-Birr) which is the highest level of morality for humans among each other.
From all this, we can conclude that attending funerals for family members or friends who are not Muslims is a social and ethical duty that we owe each other.
I would only recommend that during religious services that are invoked in a name other than God that a Muslim should not participate in that. Allah said: {For you is your religion and for me is my religion.} (Yunus 109:6)
Almighty Allah knows best.