Abu Ad-Darda [a companion and pupil of Muhammad]
"We smile in the face of some people although our hearts curse them."
A deception "allowed until the Day of Resurrection."
Thus you have a mainstream pious Islamic idea of "friendship" with non-believers.

Sura 3 - Al-E-Imran (MADINA) : Verse 54
And they (the disbelievers) schemed, and Allah schemed (against them): and Allah is the best of schemers.

Narrated Um Kulthum bint `Uqba:
That she heard Allah's Messenger () saying, "He who makes peace between the people by inventing good information or saying good things, is not a liar."

حَدَّثَنَا عَبْدُ الْعَزِيزِ بْنُ عَبْدِ اللَّهِ، حَدَّثَنَا إِبْرَاهِيمُ بْنُ سَعْدٍ، عَنْ صَالِحٍ، عَنِ ابْنِ شِهَابٍ، أَنَّ حُمَيْدَ بْنَ عَبْدِ الرَّحْمَنِ، أَخْبَرَهُ أَنَّ أُمَّهُ أُمَّ كُلْثُومٍ بِنْتَ عُقْبَةَ أَخْبَرَتْهُ أَنَّهَا، سَمِعَتْ رَسُولَ اللَّهِ صلى الله عليه وسلم يَقُولُ " لَيْسَ الْكَذَّابُ الَّذِي يُصْلِحُ بَيْنَ النَّاسِ، فَيَنْمِي خَيْرًا، أَوْ يَقُولُ خَيْرًا ".

Reference : Sahih al-Bukhari 2692
In-book reference : Book 53, Hadith 3
USC-MSA web (English) reference : Vol. 3, Book 49, Hadith 857