Question Summary:
Can we greet and reply good morning to Non-Muslims?

Question Detail:

Can we greet and reply 'good morning' to Non-Muslims ?, as I have heard a incident in which a person comes to the Prophet (pbuh) and says 'Sabah al Khayr' (good morning) and the prophet (pbuh) tells him (to the nearest meaning) that this is not our greeting, we say Assalamu alyakum. What can we answer if they (non muslims) say Good morning first ? 

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
As Muslims we are advised to develop good character and conduct to all including non-Muslims.
It is correct that Rasulullah sallahu alayhi wasalam changed the greeting of the time of jahiliyah from [1] انعم صباحا (may you have a good morning) to السلام عليكم (peace be upon you). This does not mean we cannot greet non-Muslims.
If a non-Muslim greets a Muslim with good morning, it is not prohibited to respond by saying good morning.
 
And Allah Ta’āla Knows Best
Ismail Dawoodjee
Student Darul Iftaa
Zambia
Checked and Approved by,
Mufti Ebrahim Desai.
www.daruliftaa.net 
[1] كنا فى الجاهلية نقول انعم الله انعم صباحا فلما كان الاسلام نهينا عن زالك (مرقاة ج7 ص2948 علمية)
 [2] لكن فى شرعة اذا سلم على اهل الذمة فليقل السلام على من اتبع الهدى (الرد المحتار ج6 ص412 سعيد)
محمودية ج19 ص97 فاروقية
احسن ج8 ص134 سعيد