Answered by Shaykh Faraz Rabbani
Is it alright to say “Peace be upon you” to non-Muslims?
Assalamu alaikum wa rahmatullah,
I pray that you are well, and in the best of health and spirits. May Allah grant you all good in this life and the next.
Sidi, this link deals with the details of your question, insha’Allah:
Giving Salams to Non-Muslims
It is from social propriety to greet everyone, Muslim and non-Muslim. Generally, one reserves the greeting of salam to Muslims. However, when there is need or obvious benefit in extending this greeting to non-Muslims, then the scholars have mentioned that there is no harm (and, often, much wisdom) in doing so.
And Allah alone gives success.