One of the issues that has been emphasized in our religious teachings is greeting other believers with salams. There are exceptions to this teaching though, greeting non-Muslims being one of them. In jurisprudential books, greeting non-Muslims has been deemed as makruh: "When responding to the greetings of a non-Muslim, keep it short [by saying 'alayk' or 'alaykum']."
Of course, this depends on the degree of interaction the Muslims have with them; in certain cases it might not be the best thing to greet them coldly and without feeling; this may contradict other religious teachings.
An example of these teachings that have been mentioned in the hadiths is: In response to what the Jews would say to the prophet (instead of saying 'Assalaamu Alaykum', they would say 'Assaamu Alaykum' which meant 'death be upon you' instead of 'peace be with you'), he would say: 'Alayk' (which meant [the same] to you), and when he saw some of his wives retaliating with abusive language, he said to them: "إِنَّ الْفُحْشَ لَوْ کَانَ مُمَثَّلًا لَکَانَ مِثَالَ سَوْءٍ، إِنَّ الرِّفْقَ لَمْ یوضَعْ عَلَى شَیءٍ قَطُّ إِلَّا زَانَهُ وَ لَمْ یرْفَعْ عَنْهُ قَطُّ إِلَّا شَانَه" which translates into: "If cursing and abusive language were to be embodied, they would make a very ugly statue. Anything that kindness and gentleness are added to is adorned, and anything deprived of kindness and gentleness becomes ugly and unpleasant."
Therefore, with those non-Muslims whom we are not at war with, and due to necessity, we interact and have relations with, it is better to act in a way that doesn't give a bad impression of Muslims and religion.
This Question has no detailed answer.
 See: Fazel Lankarani, Muhammad, Ahkame Javanan, p. 182, Amir Qalam Press, Qum, 1427 AH; Tabatabai Yazdi, Sayyid Muhammad Kadhim, Al-Urwat al-Wuthqa ma'a Ta'liqat al-Fazel, vol. 1, p. 536, Aimmah Athaar Jurisprudential Center, Qum, without date of publication.
 Kulayni, Muhammad ibn Yaqub, vol. 2, p. 648, Daar al-Kutub al-Islamiyyah, Tehran, 1365 (solar).