Here is the islamic ruling of Grand Ayatullah sistani Based On Holy quran about greeting’s and being around non muslim’s
Friendship with non-Muslims
A Muslim is allowed to take non-Muslims for acquaintances and friends, to be sincere towards them and they be sincere towards him, to help one another in fulfilling the needs of this life. Almighty Allãh has said in His noble Book: “Allãh does not forbid you in regard to those who have not made war against you on account of (your) religion, and have not driven you forth from your homes, that you show them kindness and deal with them justly; surely Allãh loves the doers of justice.” (60:
When these kinds of friendship produce good results, it guarantees that the non-Muslim friend, neighbour, or colleague and business partner will know about the values of Islam, and it will bring him closer to this upright religion. The Prophet said to Imam ‘Ali, “If Allãh guides through you a single person from His servants, that is better for you than anything upon which the Sun shines from the East to the West.”An-Nuri, Mustadraku ‘l-Wasa’il, vol. 12, p. 241.
Grand Ayatullah said…..It is permissible to greet Ahlul Kitãb (the Jews and the Christians, etc) and also the non-Ahlul Kitãb on the occasions they celebrate like the New Year, Christmas, Easter, and the Passover.
http://www.islam-laws.com/books/codeofpracticeforwest/39.htm#55t
Message of Peace 
This is another example. Such type of things should be circulated and propogated extensively to remove the misconception of Muslims in general and even in shias that Muslims should not greet non muslims etc.
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