The Quran

لا يَتَّخِذِ المُؤمِنونَ الكافِرينَ أَولِياءَ مِن دونِ المُؤمِنينَ ۖ وَمَن يَفعَل ذٰلِكَ فَلَيسَ مِنَ اللَّهِ في شَيءٍ إِلّا أَن تَتَّقوا مِنهُم تُقاةً ۗ وَيُحَذِّرُكُمُ اللَّهُ نَفسَهُ ۗ وَإِلَى اللَّهِ المَصيرُ

Muhammad Asad

LET NOT the believers take those who deny the truth for their allies in preference to the believers¹ - since he who does this cuts himself off from God in everything - unless it be to protect yourselves against them in this way.² But God warns you to beware of Him: for with God is all journeys' end.

I.e., in cases where the interests of those "deniers of the truth" clash with the interests of believers (Manar 111, 278). Regarding the deeper implications of the term "allies" (awliya'), see 4:139 and the corresponding note.
Lit., "unless you fear from them something that is to be feared". Zamakhshari explains this phrase as meaning, "unless you have reason to fear that they might do something which ought to be guarded against" - obviously referring to situations in which "those who deny the truth" are more powerful than the Muslims, and are therefore in a position to damage the latter unless they become their "allies" in a political or moral sense.