Saying 'salams' to non-Muslims is permissible!

I first heard the explanation for this issue from Imam Yassir Fazaga during one of his classes (may Allah reward him for them), and I think this article says it well. Excerpts below:

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 `Abbâs, Ibn Mas`ûd, Abû Umâmah, Ibn Muhîrîz, and `Umar b. `Abd al-`Azîz. It was also the opinion of many prominent imams, including Sufyân b. `Uyaynah, al-Sha`bî, al-Awzâ`î, and al-Tabarî. Recently, this opinion has been adopted by al-Sayyid Rashîd Ridâ’ in Tafsîr al-Manâr and al-Shinqîtî in Adwâ’ al-Bayân.

This view is in harmony with how the Qur’ân represents the Islamic greeting of peace as a universal greeting.

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!’ ” [Sûrah al-Furqân: 63]

There are many scholars who hold the view that it is either disliked or prohibited for Muslims to initiate the greeting of salâm with non-Muslims. They rely on the following hadîth as evidence: “Do not initiate the salutation of ‘Peace’ with the Jews and Christians.” [Sahîh Muslim (2167)]

However, this hadîth 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 Banû Qurayzah. This is established by another authentic hadîth 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-Tabarânî al-Kabîr (22/291). See also Musnad Ahmad (16844 & 17584)]

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