It is perfectly alright for a non-Muslim to greet another person with the Islamic greeting of peace: “Al-Salām `Alaykum.”
However, Muslims receive special blessings for the practice of offering this greeting, since the blessing one earns by offering the greeting to someone else comes from emulating the example – the Sunnah – of the Prophet (peace be upon him) as a matter of faith.
It is also permissible for a Muslim to greet a non-Muslim with this greeting. This was asserted by a number of Companions and Successors, including Ibn `Abbās, Ibn Mas`ūd, Abū Umāmah, Ibn Muhīrīz, and `Umar b. `Abd al-`Azīz. It was also the opinion of many prominent imams, including Sufyān b. `Uyaynah, al-Sha`bī, al-Awzā`ī, and al-Tabarī.
Recently, this opinion has been adopted by al-Sayyid Rashīd Ridā’ in Tafsīr al-Manār and al-Shinqītī in Adwā’ al-Bayān.
This view is in harmony with how the Qur’ān represents the Islamic greeting of peace as a universal greeting.
Allah says: “O you who believe! Enter not houses other than your own without first announcing your presence and invoking peace upon the folk thereof. That is better for you, that you may be heedful.” [Sūrah al-Nūr: 27]
Allah says: “And when they hear idle talk they turn aside from it and say: We shall have our deeds and you shall have your deeds; peace be on you, we do not desire the ignorant.” [Sūrah al-Qasas: 55]
He says: “And the servants of (Allah) Most Gracious are those who walk on the earth in humility, and when the ignorant address them, they say, ‘Peace!’ ” [Sūrah al-Furqān: 63]
He also says: “Consider his cry: ‘O my Lord! surely they are a people who do not believe’. So turn away from them and say, ‘Peace’, for they shall soon come to know.” [Sūrah al-Zukhruf: 88-89]
And: “(The father) replied: ‘Do you hate my gods, O Abraham? If you forbear not, I will indeed stone you: Now get away from me for a good long while!’ Abraham said: ‘Peace be on thee: I will pray to my Lord for thy forgiveness: for He is to me Most Gracious’.” [Sūrah Maryam: 47]
There is also ample hadīth evidence to establish the universality of this greeting.
The Prophet (peace be upon him) said: “Greet with ‘Peace’ those whom you know and those whom you do not know.” [Sahīh al-Bukharī (12) and Sahīh Muslim (39)]
The Prophet (peace be upon him) also informed us that when Allah created Adam, He commanded him: “Go to that assembly – and they were an assembly of seated angels – and listen to how they greet you. Indeed, it is your greeting and the greeting of your descendants. He said: “Peace be upon you.” They said: “Peace be upon you and Allah’s mercy.” [Sahīh al-Bukhārī (3326 & 6227) and Sahīh Muslim (2841)]
The Prophet (peace be upon him) also said: “Spread the greeting of peace.” [Sunan al-Tirmidhī (1854) and Sahīh Ibn Hibbān (489)]
There are scholars who have held the view that it is either disliked or prohibited for Muslims to initiate the greeting of salām (peace) with non-Muslims. They rely on the following hadīth as evidence: “Do not initiate the salutation of ‘Peace’ with the Jews and Christians.” [Sahīh Muslim (2167)]
However, this hadīth relates to a state of hostilities which had erupted at that time against the Muslims. It was, in fact, at the time of the campaign against Banū Qurayzah. This is established by another authentic hadīth where the Prophet (peace be upon him) said: “We are going forth in the morning against a group of Jews, so do not initiate the greeting of ‘Peace’ with them. [Musnad Ahmad (26695) and Mu`jam al-Tabarānī al-Kabīr (22/291). See also Musnad Ahmad (16844 & 17584)]
Ibn Hajar al-`Asqalānī relates the same from al-Bukhārī’s al-Adab al-Mufrid and from Sunan al-Nasā’ī while discussing this topic in Fath al-Bārī (11/39).
This means that hadith is evidence that the normal practice is to initiate the greeting of peace with non-Muslims, since the Prophet had to tell his Companions to stop doing so with that particular group of people under those particular circumstances.
Therefore, the greeting of peace can and should be used for all people. This view has been held by eminent scholars of all schools of thought. It is certainly the opinion to adopt when living at peace in the company of non-Muslims. Those Muslims who are living in non-Muslim countries should have a concern for outreach. Greeting all people in the best of manner without showing discrimination is an essential etiquette of reaching out to others.
It is also important to understand that those who have disapproved of Muslims greeting non-Muslims with the greeting of “salām” limited this only to initiating the greeting, not to replying to it. When a non-Muslim greets a Muslim with “al-Salām `alaykum”, then it is obligatory for the Muslim to return the greeting.
This is because Allah says: “When you are greeted with a greeting, greet back with better than it or return it. Lo! Allah takes count of all things.” [Sūrah al-Nisā’: 86]
This verse shows that it is preferable to offer a better, more generous greeting and it is obligatory to do justice and to at least return the same. Ibn Qayyim al-Jawziyyah explains in Ahkām Ahl al-Dhimmah that this ruling certainly applies to non-Muslims as well as Muslims.
And Allah knows best.