بسم الله الرحمن الرحيم
Muslims must assume good etiquette and noble conduct with all those whom they meet. Allah ﷻ Said:
وَقُولُوا لِلنَّاسِ حُسْنًا
“…And speak to people with husna…” 
Ibn Abbas رضي الله عنه gave a profound example in the length he would go to show such husna. He said:
لو قال لي فرعون بارك الله فيك، لقلت وفيك!
“If Fir’awn said to me, ‘barakAllahu feek’ (Allah bless you), I would reply, ‘wa feek’ (and to you).” 
Greeting non-Muslims for example, is from good manners – especially when they initiate it. Muslims need to be consistent in maintaining positive interaction and ensure others feel at ease. Expounding this principle, Dr. ‘Abdullah ibn Ibraheem al-Luhaydan said that making du’a for non-Muslims (living in our midst) is regulated by Shar’iah and is from one of the important ways of projecting tolerance in Islam. One of the main advantages is that you look to treat all humanity with dignity and care; and supplicate for them (with the intention) to win over their hearts (to Islam)… 
There is also no reason why Muslims should not cooperate with non-Muslims with regard to establishing a common truth and combating falsehood, in supporting the downtrodden and oppressed and warding off danger from mankind, such as combating pollution or protecting the environment, combing relief work from natural disasters and diseases and so on. Islam forbids harming others and also reciprocating any harm (لا ضرر ولا ضرار); this is a legal maxim in Islamic law. Muslims should be particularly careful to protect those within their communities no matter who they are, and even the animals. This is the most pleasant way to live your lives, as Al-Hasan Al-Basri said:
إِنْ سَرَّكُمْ أَنْ تَسْلَمُوا وَيَسْلَمَ لَكُمْ دِينُكُمْ فَكُفُّوا أَيْدِيَكُمْ عَنْ دِمَاءِ النَّاسِ وَكُفُّوا أَلْسِنَتَكُمْ عَنْ أَعْرَاضِهِمْ وَكُفُّوا بُطُونَكُمْ عَنْ أَمْوَالِهِمْ
“If you be pleased to be safe and for your religion to be safe for you, then restrain your hands from injuring people, restrain your tongues from harming their honour, and restrain your stomachs from consuming their wealth.” 
 Al-Baqarah, 83.
 Saheeh Al-Adab al-Mufrad, 848; see also ‘Silsilat as-Saheehah’, 2/322 where the chain has been declared to be authentic.
 13 سماحة الإسلام في معاملة غير المسلمين
 See ‘Makarim al-Akhlaaq, Khara’iti’.