Riyad Us-Saliheen (Gardens of the Righteous)

Chapter 138
Greeting the non-Muslims and Prohibition of taking an Initiative

866. Abu Hurairah (May Allah be pleased with him) reported: The Messenger of Allah (PBUH) said, "Do not greet the Jews and the Christians before they greet you; and when you meet any one of them on the road, force him to go to the narrowest part of it.''
[Muslim].

Commentary: This Hadith prohibits Muslims from greeting non-Muslims first. It also tells us that when the road is crowded, we should use the middle of the road and let the non-Muslims use its sides. This Hadith shows the dignity of Muslims and the disgrace and humiliation of the non-Muslims.

867. Anas (May Allah be pleased with him) reported: Messenger of Allah (PBUH) said, "When the people of the Book greet you (i.e., by saying `As-Samu `Alaikum,' meaning death be upon you), you should respond with: `Wa `alaikum' [The same on you (i.e., and death will be upon you, for no one will escape death)].''
[Al-Bukhari and Muslim].

868. Usamah bin Zaid (May Allah be pleased with him) reported: The Prophet (PBUH) passed by a mixed company of people which included Muslims, polytheists and Jews, and he gave them the greeting (i.e., saying As-Salamu `Alaikum).
[Al-Bukhari and Muslim].

Commentary:  If there is a mixed assembly of Muslims and non-Muslims, one should utter greeting to it but consider Muslims as one's addressees.