What is the ruling on answering the greeting of Christians?

Question 417: What is the ruling of Islaam on answering the greeting of Christians, following their funerals, and offering them condolences?

Answer: If a Kaafir (disbeliever) greets a Muslim, the latter should reply by saying “The same to you” as mentioned in the Saheeh (sound) Hadeeth in which the Prophet (peace be upon him) said, When the People of the Book greet you, you should say, “The same to you.” However, it is not permissible for a Muslim to follow the funeral of a Kaafir, for this is considered an act of loyalty to them which is Haraam (prohibited). However, consoling them is acceptable if there is a Shar`ee (Islaamically lawful) probable interest. In this case, they should say, “I offer you my condolences, may your distress be relieved,” but they should not say, “May Allaah forgive your deceased,” for seeking forgiveness for a Mushrik (one associating others in worship with Allaah) is not permissible... read more here.