How should I greet non-Muslims?

“The correct pronounciation of Salam is As Salaamu Alaikum. It is incorrect to greet with Shalom Aleikhem- as that is a greeting of the Jews. The greeting As Salam alaikum is specifically for Muslims.”

“You may greet with the words: You are a slave, so remain a slave. Don't assume the role of a master. Allah Ta`ala is not only the master, He is the creator, He is the supreme control, He knows the past and future. Islam does not say that we treat the kaafir like an animal.”

“In the Hadith, we are prohibited from making Salaam to the Kuffar. Rasulullah Salallahu Alaihi Wasallam is reported to have said, “Do not initiate Salaam with the Jews and Christians.” [Re:- Muslim Hadith no. 2167] It is on this basis that the Fuqaha have written that it is Makrooh to make Salaam to non-Muslims.”