Tafsir al-Jalalayn, Muhammed Asad and Maulana Muhammed Ali commentary of the Quran say these passages refer to Banu Asad and Ghatafan tribes. These tribes have in a number of occasions been hostile and sided with enemies of the Prophet (p). And waged war against the Muslims.
Others, such as Ibn Kathir and Maududi’s Quran commentary, say that the verse refers to the hypocrite Muslims who had accepted the message of Islam in Makkah but they never emigrated to Madinah. Further, they mention that they sided with the enemies of the Muslims in Makkah i.e., sided in the sense fighting and persecuting Muslims.
They were a bunch of very difficult persons to deal with, because outwardly they prayed, recited the Kalimah (article of Islamic faith), and fasted in the month of Ramadan, but at the same time they did the worst things against the true Muslims.
4:89 They wish you would disbelieve as they disbelieved so you would be alike. So do not take from among them allies until they emigrate for the cause of Allah. But if they turn away, then seize them and kill them wherever you find them and take not from among them any ally or helper.
4:90 Except for those who take refuge with a people between yourselves and whom is a treaty or those who come to you, their hearts strained at [the prospect of] fighting you or fighting their own people. And if Allah had willed, He could have given them power over you, and they would have fought you. So if they remove themselves from you and do not fight you and offer you peace, then Allah has not made for you a cause [for fighting] against them.
4:91 You will find others who wish to obtain security from you and [to] obtain security from their people. Every time they are returned to [the influence of] disbelief, they fall back into it. So if they do not withdraw from you or offer you peace or restrain their hands, then seize them and kill them wherever you overtake them. And those – We have made for you against them a clear authorization.
In 4:89 God Almighty turned the hypocrites back to unbelief for what they did (Maududi). Furthermore, the Muslims were commanded 1400 years ago to catch hold of those hypocrites who were actually engaged warfare against the Muslims then.
4:90 shows that the fighting mentioned here were not against innocents, but aimed at those who were actively fighting against the Muslims, 1400 years ago. The verse says, if they cease from hostilities, and remove themselves, not siding with the enemies, and offer peace that they be left alone.
In 4:91 it emphasizes what has been mentioned already, that there are those who will be asking for security but at the same time they refrained from offering peace to the Muslims, by not stopping their hostilities. The Muslims 1400 years ago were commanded that they be caught and dealt with, as a result of their ongoing hostilities, and the fighting they were involved in against the Muslims.
All these verses speak of events that relate to individuals (or groups) who actively fought and harmed the Muslims.
Malik Ghulam Farid:
“645. The reference is to the Bedouin tribes of the desert. The Qur’an forbids Muslims to have anything to do with them, or make friends with them or seek their help.
646. As Qatl is also used in the sense of severing all social contacts (2:62), the expression Uquluhum may also mean, ‘have nothing to do with them.’ This meaning of the expression finds support from the words, ‘take no friend nor helper from among them.’
647. The reference seems to be the two tribes, Asad and Ghatafan who had no treaty of alliance with the Muslims. They played a double game and awaited their opportunity. When invited by their people to join them in fighting against the Muslims, they readily accepted the invitation. The directions contained in these verses come into operation when a virtual state of war exists and danger stalks along the land.
648. By Fitnah is here meant, war with the Muslims.
649. As when actual or virtual state of war exists there is the likelihood that a Muslim may be killed by another Muslim by mistake, the present verse gives a timely warning to Muslims to be always on their guard against such an eventuality.” 
Maulana Muhammad Ali:
“90a. This verse explains the previous one, showing clearly that even waverers were not to be killed or fought against if they refrained from fighting, though they may have gone over to disbelief after accepting Islam. The commentators agree that the persons referred to in this verse were disbelievers and not Muslims, and they are generally supposed to have been the Banu Mudlaj (Bd). Note also that we have here the clear injunction that if any people offered peace, they were not to be fought against.
91a. By mischief, or fitnah, is meant war with the Muslims (Rz). Two tribes, Asad and Ghatfan, came to the Muslims and showed an inclination to remain at peace, but when they went back and their people invited them to join them in fighting with the Muslims, they responded to the call. Such people could not be trusted. The importance of these directions in time of war, when the Muslims were hemmed in on all sides by enemies, can hardly be overestimated.” 
“106 Lit., “two parties”.
107 Lit., “seeing that God has thrown them back in result of what they have earned”. There are various conjectures, almost all of them of a historical nature, as to the identity of these hypocrites. Some of the commentators think that the verse refers to the hypocrites at Medina in the early years after the hijrah;
others (e.g., Tabari) prefer the view expressed by Ibn ‘Abbas, according to whom this refers to certain people of Mecca who, before the hijrah, outwardly accepted Islam but secretly continued to support the pagan Quraysh.
It seems to me, however, that there is no need to search after “historical” interpretations of the above verse, since it can easily be understood in general terms. The preceding verse speaks of God, and stresses His oneness and the obvious truth inherent in His revealed message, as well as the certainty of judgment on Resurrection Day.
“How, then,” continues the argument, “could you be of two minds regarding the moral stature of people who go so far as to pay lip-service to the truth of God’s message and are, nevertheless, not willing to make a sincere choice between right and wrong?”
108 See surah 2, verse 218, as well as note on verse 97 of this surah.
109 I.e., any of those who have not “forsaken the domain of evil” and are wavering between belief and disbelief.
110 Lit., “if God had so willed, He would indeed have given them power over you, whereupon…”, etc.- implying that only the lack of requisite power, and not true good will, causes them to refrain from making war on the believers.
111 Lit., “God has given you no way against them”: a reference to the ordinance laid down in verse 86 above.
112 Lit., “whenever they are returned to temptation (fitnah), they are thrown back into it” or thrown headlong into it”.
113 Lit., “that We have given you clear authority (sultan)” – a solemn reiteration of the ordinance which permits war only in self-defence (cf. 2:190 ff. as well as the corresponding notes).” 
Tafsir Ibn Kathir:
“… (They wish that you reject faith, as they have rejected, and thus that you all become equal.) means, they wish that you fall into misguidance, so that you and they are equal in that regard. This is because of their extreme enmity and hatred for you. Therefore, Allah said, …
Combatants and Noncombatants … (Except those who join a group, between you and whom there is a treaty (of peace),) meaning, except those who join and take refuge with a people with whom you have a pact of peace, or people of Dhimmah, then treat them as you treat the people with whom you have peace.
This is the saying of As-Suddi, Ibn Zayd and Ibn Jarir. In his Sahih, Al-Bukhari recorded the story of the treaty of Al-Hudaybiyyah, where it was mentioned that whoever liked to have peace with Quraysh and conduct a pact with them, then they were allowed.
Those who liked to have peace with Muhammad and his Companions and enter a pact with them were allowed. … (or those who approach you with their breasts restraining) referring to another type of people covered by the exclusion from fighting.
They are those who approach the Muslims with hesitation in their hearts because of their aversion to fighting the Muslims. They do not have the heart to fight with the Muslims against their own people. Therefore, they are neither with nor against Muslims.
(Had Allah willed, indeed He would have given them power over you, and they would have fought you.) meaning, IT IS FROM ALLAH’S MERCY THAT HE HAS STOPPED THEM FROM FIGHTING YOU. (SO, IF THEY WITHDRAW FROM YOU, AND FIGHT NOT AGAINST YOU, AND OFFER YOU PEACE,) MEANING, THEY REVERT TO PEACE, … (then Allah has opened no way for you against them), YOU DO NOT HAVE THE RIGHT TO KILL THEM, AS LONG AS THEY TAKE THIS POSITION.
This was the position of Banu Hashim (the tribe of the Prophet ), such as Al-`Abbas, who accompanied the idolators in the battle of Badr, for they joined the battle with great hesitation. This is why the Prophet commanded that Al-`Abbas not be killed, but only captured. Allah’s statement, (You will find others that wish to have security from you and security from their people.) refers to a type of people who on the surface appear to be like the type we just mentioned.
However, the intention of each type is different, for the latter are hypocrites. They pretend to be Muslims with the Prophet and his Companions, so that they could attain safety with the Muslims for their blood, property and families.
However, THEY SUPPORT THE IDOLATORS IN SECRET and worship what they worship, so that they are at peace with them also. THESE PEOPLE HAVE SECRETLY SIDED WITH THE IDOLATORS, just as Allah described them, (Every time they are sent back to Fitnah, they yield thereto.) meaning, they dwell in Fitnah.
As-Suddi said that the Fitnah mentioned here refers to Shirk. Ibn Jarir recorded that Mujahid said that the Ayah was revealed about a group from Makkah who used to go to the Prophet ﴿ in Al-Madinah﴾ pretending to be Muslims. However, when they went back to Quraysh, they reverted to worshipping idols. They wanted to be at peace with both sides.
Allah commanded they should be fought against, UNLESS THEY WITHDRAW FROM COMBAT AND RESORT TO PEACE. This is why Allah said, (If they withdraw not from you, nor offer you peace) meaning, REVERT TO PEACEFUL AND COMPLACENT BEHAVIOR, (nor restrain their hands) REFRAIN FROM FIGHTING YOU, (take (hold of) them), capture them, (and kill them wherever you Thaqiftumuhum.), wherever you find them, (In their case, We have provided you with a clear warrant against them), meaning an unequivocal and plain warrant.” 
“They long, they wish, that you should disbelieve as they disbelieve, so then you, and they, would be equal, in unbelief; therefore do not take friends from among them, associating with them, even if they should [outwardly] manifest belief, until they emigrate in the way of God, a proper emigration that would confirm their belief; then,
If they turn away, and remain upon their ways, take them, as captives, and slay them wherever you find them; and do not take any of them as a patron, to associate with, or as a helper, to assist you against your enemy.
Except those who attach themselves to, [who] seek refuge with, a people between whom and you there is a covenant, a pledge of security for them and for whoever attaches himself to them, in the manner of the Prophet’s (s) covenant with Hilal b. ‘Uwaymir al-Aslami; or, those who, come to you with their breasts constricted, dejected, about the prospect of
fighting you, [being] on the side of their people, or fighting their people, siding with you, in other words, [those who come to you] REFRAINING FROM FIGHTING EITHER YOU OR THEM, THEN DO NOT INTERFERE WITH THEM, NEITHER TAKING THEM AS CAPTIVES NOR SLAYING THEM …
Had God willed, to give them sway over you, He would have given them sway over you, by strengthening their hearts, so that assuredly they would have fought you: but God did not will it and so He cast terror into their hearts. And so IF THEY STAY AWAY FROM YOU AND DO NOT FIGHT YOU, AND OFFER YOU PEACE, RECONCILIATION, that is, [if] they submit, then God does not allow you any way against them, [He does not allow you] a means to take them captive or to slay them.
You will find others desiring to have security from you, by manifesting belief before you, and security from their own people, through unbelief, when they return to them, and these were [the tribes of] Asad and Ghatafan; yet whenever THEY ARE RETURNED TO SEDITION, [whenever] they are summoned to idolatry, they are overwhelmed by it, falling into it in the worst of ways.
So, IF THEY DO NOT STAY AWAY FROM YOU, BY REFRAINING FROM FIGHTING YOU, AND, DO NOT, OFFER YOU PEACE, AND, DO NOT, RESTRAIN THEIR HANDS, FROM YOU, then take them, as captives, and slay them wherever you come upon them, [wherever] you find them; against them We have given you clear warrant, a clear and manifest proof for you to slay them and capture them, on account of their treachery.” 
Tanwir al-Miqbas min Tafsir Ibn ‘Abbas:
“(They long that you should disbelieve) in Muhammad and the Qur’an (even as they disbelieve, that ye may be upon a level (with them)) in following idolatry. (So choose not friends from them) in religion or for seeking assistance and backing (till they forsake their homes) until they believe again and migrate (in the way of Allah) in obedience of Allah; (if they turn back) from faith and migration (then take them) as prisoners (and kill them wherever you find them) in the
Sacred Precinct or anywhere else, (and choose no friend) in religion or for seeking assistance and backing (nor helper) a protector (from among them), Allah then made an exception, saying: (Except those) among the ten men who fled to Mecca (who seek refuge with a people) i.e. the people of Hilal Ibn ‘Uwaymir al-Aslami (between whom and you there is
a covenant) a pact and peace, (or (those who)) the people of Hilal (come unto you because their hearts forbid them to make war) they come to you because they are annoyed at the huge cost they have to pay due to this pact (on you or make war on their own folk) due to their ties of kinship. (Had Allah willed He could have given them power over you)
i.e. the people of Hilal Ibn ‘Uwaymir (so that assuredly they would have fought you) together with their people upon the conquest of Mecca. (So, IF THEY HOLD ALOOF FROM YOU AND WAGE NOT WAR AGAINST YOU) upon the conquest of Mecca (and offer you peace) THEY SUBMIT TO YOU THROUGH PEACE AND HONOURING THE PACT
THEY MADE, (ALLAH ALLOWETH YOU NO WAY AGAINST THEM) HE DOES NOT GIVE YOU ANY EXCUSE FOR KILLING THEM. (You will find others) other than the people of Hilal, Asad and Ghatafan for example (who desire that they should have security from you) they desire that their persons and wealth and families be safe from you by the
declaration of “there is no god but Allah”, (and security from their own folk) and desire to be safe from their clan by adhering to disbelief. (So often as they are returned to hostility) to idolatry (they are plunged therein) they revert to it.
(IF THEY KEEP NOT ALOOF FROM YOU) UPON THE CONQUEST OF MECCA (NOR OFFER YOU PEACE) NOR SUBMIT TO YOU BY MEANS OF A TREATY (NOR HOLD THEIR HANDS) FROM FIGHTING YOU upon the conquest of Mecca, (then take them) as prisoners (and kill them wherever you find them) in the Sacred Precinct or anywhere else. (Against such) i.e. Asad and Ghatafan (We have given you clear warrant) to kill them.” 
“…Or those who come to you with their breasts constricted… That is, ‘They have become sick at heart BECAUSE OF FIGHTING YOU and fighting their people, due to their love of safety, and their inclination towards their own well-being (ʿafiya).’ This refers to the Banu Madlaj.” 
 The Holy Qur’an – Arabic Text With English Translation & Short Commentary By Malik Ghulam Farid,
Page 208 – 209
 The Holy Quran Arabic Text with English Translation, Commentary and comprehensive Introduction [Year 2002 Edition] by Maulana Muhammad Ali, page 222
 The Message of The Quran translated and explained by Muhammad Asad, page 186 – 188
 Tafsir Ibn Kathir http://www.alim.org/library/quran/AlQuran-tafsir/TIK/4/88
 Tafsir al-Jalalayn http://altafsir.com/Tafasir.asp?tMadhNo=0&tTafsirNo=74&tSoraNo=4&tAyahNo=90&tDisplay=yes&UserProfile=0&LanguageId=2
 Tanwir al-Miqbas min Tafsir Ibn ‘Abbas http://altafsir.com/Tafasir.asp?tMadhNo=0&tTafsirNo=73&tSoraNo=4&tAyahNo=91&tDisplay=yes&UserProfile=0&LanguageId=2
 Tafsir al-Tustari http://altafsir.com/Tafasir.asp?tMadhNo=0&tTafsirNo=93&tSoraNo=4&tAyahNo=90&tDisplay=yes&UserProfile=0&LanguageId=2