I don't understand, why would they react?
The greeting of peace is just for Muslims, BUT if a non-Muslim greets with peace, we give them back what they give us, but if they greet us badly, we just return what they give us as well.
It was narrated that the Prophet (peace and blessings of Allaah be upon him) said: “Do not initiate the greeting to the Jews and Christians.” (Narrated by Muslim, Kitaab al-Salaam).
The Jews used to pass by the Prophet (peace and blessings of Allaah be upon him) and say “Al-saam ‘alaykum” meaning death. So the Prophet (peace and blessings of Allaah be upon him) told us to say “Wa ‘alaykum (and also to you).” (Narrated by al-Bukhaari, Kitaab al-Adaab; Muslim, Kitaab al-Salaam).
So you should not initiate the greeting, but if he greets you and initiates the greeting, then say, “Wa ‘alaykum.” But Ibn al-Qayyim (may Allaah have mercy on him) mentioned in Ahkaam Ahl al-Dhimmah that if we know for sure that a disbeliever has said “Al-salaamu ‘alaykum,” then we may say, “Wa ‘alaykum al-salaam.”
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