Attending the funeral of a non-Muslim colleague in the church out of respect for the deceased

It is not permissible for the Muslim to attend the funeral of a kaafir or to enter their
churches, even if that is a sign of respect etc, because attending the funeral is a way of showing love and respect, and it is not permissible to
show that towards a kaafir, according to the correct view. 

Moreover the questioner says, “to attend the funeral of a non-Muslim friend” – but it is not
permissible for a Muslim to take a kaafir as a friend, because Allaah has commanded us to regard them as enemies, to shun them and to keep away
from them. This does not mean that we should not deal with them or buy and sell or form business partnerships with them. That is one thing, and
taking them as friends is another thing. Allaah says (interpretation of the meaning): 

“You (O Muhammad) will not find any people who believe in Allaah and the Last Day, making
friendship with those who oppose Allaah and His Messenger (Muhammad), even though they were their fathers or their sons or their brothers or their
kindred (people). For such He has written Faith in their hearts, and strengthened them with Rooh (proofs, light and true guidance) from Himself.
And He will admit them to Gardens (Paradise) under which rivers flow, to dwell therein (forever). Allaah is pleased with them, and they with Him.
They are the party of Allaah. Verily, it is the party of Allaah that will be the successful”

[al-Mujaadilah 58:22] 

And the Prophet (peace and blessings of Allaah be upon him) said: “Do not initiate the
greeting of salaam with the Jews and Christians, and when you meet them in the street, force them towards the narrowest part of it.” Narrated by
Imam Muslim in his Saheeh, 2167 from the hadeeth of Abu Hurayrah.