Is it proper to greet a non-Muslim with "As-Salāmu Alaykum" (Peace be upon you) or respond with "wa alaykumu s-salāmu wa rahmatu l-lāhi wa barakātuh" (may peace, mercy and blessings of God be upon you) to non-Muslims?
I do not consider myself Muslim, but I find it respectful to use these greetings to Muslims. It is not much different than I would address a Christian, except the language. Similarly I use "IN SHA' ALLAH" as I would say "God willing".
I don't want to offend anyone by using these greetings.