“You will surely find the most intense of the people in animosity toward the believers [to be] the Jews and those who associate others with Allah; and you will find the nearest of them in affection to the believers those who say, “We are Christians.” That is because among them are priests and monks and because they are not arrogant.” – Quran 5:82
The hatred by Jews and idolaters here speaks of those that were actively hostile to the Muslim community. As the early commentators of the Quran have clarified (Tafsir al-Jalalayn and Asbab Al-Nuzul by Al-Wahidi). The Jews of Madinah, Banu Qaynuqa, Banu Nadir, and Banu Qurayza were at the forefront of causing hate, and waging war against the Muslims.
The idolaters, were the first ones who started persecuting and killing Muslims in Makkah, for thirteen long years. Even when they fled persecution to Madinah, the Muslims were once again hounded by the Quraysh (read more about this here: ‘Did Quraysh Persecute Muslims When They Fled To Madinah?‘).
The present verse (5:82) does not refer to all Jews at all times, rather those who were hostile, and had inner hatred towards the Muslims, 1400 years ago.
The verse goes further, and says that the nearest to Muslims in way of affection, respect and humility are Christians. The Christians here said are referring to Abyssinian Christians for they protected the Muslims against the enemies (Tanwir al-Miqbas min Tafsir Ibn Abbas, Asbab Al-Nuzul by Al-Wahidi and Tabari (310AH).
The Muslims were allowed to practice their religion freely without persecution. These Christians were indeed the most humble, generous of any other faith, in Prophet Muhammed’s life-time.
“96 Lit., “of them”.
97 I.e., they do not believe, as do the Jews, that revelation is God’s exclusive gift to the children of Israel; and their “priests and monks” teach them that humility is the essence of all true faith. – It is noteworthy that the Qur’an does not in this context include the Christians among “those who are bent on ascribing divinity to aught beside God” (alladhina ashraku – the element of intent being expressed in the use of the past tense, similar to alladhina kafaru, alladhina zalamu, etc.):
for although, by their deification of Jesus, they are guilty of the sin of shirk (“the ascribing of divinity to anyone or anything beside God”), the Christians do not consciously worship a plurality of deities inasmuch as, theoretically, their theology postulates belief in the One God, who is conceived as manifesting Himself in a trinity of aspects, or “persons”, of whom Jesus is supposed to be one.
However repugnant this doctrine may be to the teachings of the Qur’an, their shirk is not based on conscious intent, but rather flows from their “overstepping the bounds of truth” in their veneration of Jesus (see 4:171, 5:77). Cf. in this context Razi’s remarks mentioned in note 16 on 6:23.” 
“You, O Muhammad (s), will truly find the most hostile of people to those who believe to be the Jews and the idolaters, of Mecca, because of the intensity of their disbelief, ignorance and utter preoccupation with following whims; and you will truly find the nearest of them in love to those who believe to be those who say ‘Verily, we are Christians’;
that, nearness of theirs in love to the believers is, because some of them are priests, scholars, and monks, devout worshippers, and because they are not disdainful, of following the truth, as the Jews and the Meccans are.” 
Tanwir al-Miqbas min Tafsir Ibn ‘Abbas:
“Allah then showed their enmity towards the Prophet (pbuh) and his Companions, saying: (Thou wilt find) O Muhammad (the most vehement of mankind in hostility) and most vile in speech (to those who believe) Muhammad and his Companions ((to be) the Jews) the Jews of the Banu Qurayzah, Banu’l-Nadir,
Fadak and Khaybar (and the idolaters) and the most vehement in hostility to the believers among the idolaters are the idolaters of Mecca. (And thou wilt find the nearest of them in affection) in their bond and most lenient in speech (to those who believe) Muhammad and his Companions ((to be) those who say:
Lo! We are Christians) the Negus and his followers who were 32 men; it is also said that they were 40 people in total: 32 from Abyssinia, and eight monks from Historic Syria: the monk Bahirah and his followers Abrahah, Ashraf, Idris, Tamim, Tammam, Durayd and Ayman.
(That) affection (is because there are among them priests) ascetics whose heads are shaved in the middle (and monks) secluded in monasteries who are their men of knowledge, (and because they are not proud) in believing in Muhammad and the Qur’an.” 
Asbab Al-Nuzul by Al-Wahidi:
“(Thou wilt find the most vehement of mankind in hostility to those who believe (to be) the Jews) up to His words (But those who disbelieve and deny Our revelations, they are owners of hell-fire) [5:82-86]. These verses were revealed about the Negus and his followers. Said Ibn ‘Abbas: “When he was in Mecca, the Messenger of Allah, used to fear the idolaters’ persecution of his Companions.
He therefore sent Ja‘far ibn Abi Talib and ‘Abd Allah ibn Mas‘ud, at the head of a group of his Companions, to the Negus. He said: ‘The Negus is a righteous man; he is not an oppressor and none is oppressed in his dominion. So head toward him and remain there until Allah creates relief for the Muslims’.
When they went to him, the Negus honoured them and then asked them: ‘Do you memorise anything of that which was revealed to you?’
They answered in the affirmative and then recited to him [some Qur’an,] with monks and priests surrounding him. Whenever they read a verse, the tears rolled down their cheeks due to the truth which they recognized. Allah, exalted is He, says:
(That is because there are among them priests and monks, and because they are not proud)”. … “The Messenger of Allah, sent ‘Amr ibn Umayyah al-Damri with a message to the Negus. The latter read the message of the Messenger of Allah, Allah bless him and give him peace, and then called Ja‘far ibn Abi Talib and all the Emigrants with him and he also invited priests and monks to the assembly.
He ordered Ja‘far ibn Abi Talib to recite to them from the Qur’an, and he read Surah Maryam, peace be upon her. They believed in the Qur’an and tears flowed from their eyes. It is about them that Allah, exalted is He, revealed (And thou wilt find the nearest of them in affection to those who believe (to be) those who say: Lo! We are Christians) up to His words (Inscribe us as among the witnesses)”. 
 The Message of The Quran translated and explained by Muhammad Asad, page 240
 Tafsir al-Jalalayn http://altafsir.com/Tafasir.asp?tMadhNo=0&tTafsirNo=74&tSoraNo=5&tAyahNo=82&tDisplay=yes&UserProfile=0&LanguageId=2
 Tanwir al-Miqbas min Tafsir Ibn ‘Abbas http://altafsir.com/Tafasir.asp?tMadhNo=0&tTafsirNo=73&tSoraNo=5&tAyahNo=82&tDisplay=yes&UserProfile=0&LanguageId=2
 Asbab Al-Nuzul by Al-Wahidi http://altafsir.com/Tafasir.asp?tMadhNo=0&tTafsirNo=86&tSoraNo=5&tAyahNo=82&tDisplay=yes&UserProfile=0&LanguageId=2