Question :
Is it permissible for a Muslim to greet a non-Muslim with "As-Salaam-Alaikum" or should another greeting be used, such as 'Marhabah" "Hello"?
The Answer :
Praise be to Allah, the Lord of the Worlds.
Islamic Sharia urges Muslims to treat people in general with kindness and to respect their privacy; particularly the People of the Book who are peaceful to Muslims. These should be dealt with justly and kindly, because Allah, the Almighty says, "God forbids you not, with regard to those who fight you not for (your) Faith nor drive you out of your homes, from dealing kindly and justly with them: for God loveth those who are just."{Al-Mumtahanah, 8}.In addition, the Messenger of Allah (Blessings and peace of Allah be upon him) said: "Beware, if anyone wrongs a contracting man, or diminishes his right, or forces him to work beyond his capacity, or takes from him anything without his consent, I shall plead for him on the Day of Judgment."{Related by Abu Dawoud}.
This kind treatment could take the form of a social visit, and the like. It is proven in Saheeh al-Bukhaari and elsewhere that a Jewish boy used to serve the Prophet (Blessings and peace of Allah be upon him).On one occasion he fell sick and the Prophet (Blessings and peace of Allah be upon him) visited him and invited him to Islam.
Islam calls for love, affability, and observance of good ties regardless of color, race or religion, and the provisions of Sharia are adaptable with new matters and customary practices. From the time of the Prophet (Blessings and peace be upon him) until now, Christians have been living in Muslim countries in peace and security.Therefore, there is no harm in greeting them with any greeting including "As-Salaam-Alaikum". Scholars have based this view, permissibility of greeting non-Muslims, on narrations of some Companions, such as Ibn Mas`oud and Ibn Abbas. Ibn Hajar states in Fateh Al-Bari {11/45}, "It was reported that Al-A`wza`i said that if you greeted so did the righteous and if you didn`t greet so didn`t the righteous."
In his Musanaf, Ibn Shaibah narrated that Ibn Abbas (May Allah be pleased with him) said: "Whoever greeted you from the creation of Allah then return it back even if he was a Jew, a Magian, or a Christian."
However, the narration in which the Prophet (Blessings and peace be upon him) said "I will ride to the Jews tomorrow. Do not give them the greeting first. If they greet you, then say, 'and on you.'"{Ahmad} pertains to a particular incident. The Prophet (Blessings and peace be upon him) said so when he was heading to punish Bani Qhoraidah for their treason and breaking their pledge of allegiance to the Muslims. In conclusion, it is permissible for a Muslim to greet a non-Muslim first, because this is a controversial issue amongst scholars. The ones who prohibited this have based their view on evidence amenable to Ijtihad. And Allah the Almighty knows best.