Firstly: 

Islam urges us to be tolerant and forgive others. This is indicated in both the Qur’aan and the Sunnah. Indeed, one of the features of Islam is that it is deen al-rahmah (the religion of mercy). By the same token the Muslim should be easy going, not one who puts others off; he should forgive when he is able to take revenge and be tolerant when people make mistakes.  

Allaah says (interpretation of the meaning): 

“Many of the people of the Scripture (Jews and Christians) wish that if they could turn you away as disbelievers after you have believed, out of envy from their ownselves, even after the truth (that Muhammad is Allaah’s Messenger) has become manifest unto them. But forgive and overlook, till Allaah brings His Command. Verily, Allaah is Able to do all things”

[al-Baqarah 2:109] 

“So, because of their breach of their covenant, We cursed them and made their hearts grow hard. They change the words from their (right) places and have abandoned a good part of the Message that was sent to them. And you will not cease to discover deceit in them, except a few of them. But forgive them and overlook (their misdeeds). Verily, Allaah loves Al‑Muhsinoon (good‑doers”

[al-Maa’idah 5:13] 

“O you who believe! Verily, among your wives and your children there are enemies for you (who may stop you from the obedience of Allaah); therefore beware of them! But if you pardon (them) and overlook, and forgive (their faults), then verily, Allaah is Oft‑Forgiving, Most Merciful”

[al-Taghaabun 64:14]

So this forgiveness of the kaafirs should be for the sake of seeking reward with Allaah and softening the hearts of the kaafirs to the idea of entering the religion of Allaah. This is a kind of gentleness and tolerance that is encouraged and is aimed at achieving great things, namely reward from Allaah and encouraging the kaafirs to enter the religion of Islam. For the attitude of the Muslims conquered the hearts of many of the mushrikeen before the Muslims’ swords and cavalry conquered their strongholds, and they entered the religion of Allaah in crowds, seeking whatever it was in this religion that created such a good attitude in its people. 

Allaah says concerning this (interpretation of the meaning): 

“And by the Mercy of Allaah, you dealt with them gently. And had you been severe and harsh‑hearted, they would have broken away from about you; so pass over (their faults), and ask (Allaah’s) forgiveness for them; and consult them in the affairs. Then when you have taken a decision, put your trust in Allaah, certainly, Allaah loves those who put their trust (in Him)”

[Aal ‘Imraan 3:159]

The mercy, kindness and gentleness of the Messenger of Allaah (peace and blessings of Allaah be upon him) was the reason why people entered the religion of Allaah. If the Messenger of Allaah (peace and blessings of Allaah be upon him) had not been so kind and gentle, he would have put off the people around him, and they would have left him and not believed in his message. 

It was narrated from ‘Urwah ibn al-Zubayr that ‘Aa’ishah (may Allaah be pleased with her), the wife of the Prophet (peace and blessings of Allaah be upon him) said: A group of Jews entered upon the Messenger of Allaah (peace and blessings of Allaah be upon him) and said, “Al-saam ‘alaykum.” (al-saam means death). ‘Aa’ishah said: “I understood them, and said, ‘Wa ‘alaykum al-saam wa’l-la’nah (and upon you be death and curses).’ But the Messenger of Allaah (peace and blessings of Allaah be upon him) said, ‘Wait, O ‘Aa’ishah, for Allaah loves kindness in all things.’ I said, ‘O Messenger of Allaah, did you not hear what they said?’ The Messenger of Allaah (peace and blessings of Allaah be upon him) said: ‘I said, “Wa ‘alaykum (and also unto you).”’” 

Narrated by al-Bukhaari, 5678; Muslim, 2164 

Ibn Hajar said, commenting on this hadeeth: 

Because the Jews at that time were people with whom the Muslims had a treaty, so it seems that this was for the purpose of maintaining harmony with them. 

Fath al-Baari, 11/43 

Secondly: 

Allaah has given the Muslim permission, if aggression is committed against him, to settle the score, but He encourages him to forgive. Allaah says (interpretation of the meaning): 

“The recompense for an evil is an evil like thereof; but whoever forgives and makes reconciliation, his reward is with Allaah. Verily, He likes not the Zaalimoon (oppressors, polytheists, and wrongdoers).

And indeed whosoever takes revenge after he has suffered wrong, for such there is no way (of blame) against them.

The way (of blame) is only against those who oppress men and rebel in the earth without justification; for such there will be a painful torment.

And verily, whosoever shows patience and forgives, that would truly be from the things recommended by Allaah”

[al-Shoora 42:40-43]

“Allaah does not like that the evil should be uttered in public except by him who has been wronged. And Allaah is Ever All‑Hearer, All‑Knower”

[al-Nisa’ 4:148]

But we should note that the Muslim should forgive any wrong done to him by a kaafir in such a way that does not cause him humiliation, because the Muslim should be proud. Allaah has honoured him and he should feel proud of that and take that as his attitude, because if he is proud then Islam and all the Muslims are honoured. But if this forgiveness will lead to humiliation, then the Muslim has to settle the score. Concerning that Allaah says (interpretation of the meaning): 

“And those who, when an oppressive wrong is done to them, take revenge”

[al-Shoora 42:39]

Imam Ibn Rajab al-Hanbali said, commenting on this verse: 

With regard to the phrase “And those who, when an oppressive wrong is done to them, take revenge” – this does not contradict the idea of forgiveness, because taking revenge may mean demonstrating the ability to take revenge, then one may forgive after that, in which case forgiveness will come in a better context. Al-Nakha’i said concerning this verse: They do not like to be humiliated, so if they are in a position to settle the score, then they will forgive. Mujaahid said: They did not like for the believer to let himself be humiliated, which would lead the evildoers to feel contempt for him. 

If the believer is wronged, then he should show that he is able to take revenge, then he should forgive after that. Many of the salaf did that, including ‘Ata’, Qutaadah and others. 

Jaami’ al-‘Uloom wa’l-Hukam, 1/179 

Hence forgiveness is not good in all cases, rather it may be blameworthy if it results in humiliation of the Muslim or encourages the aggressor even further, etc. 

Allaah has referred to that in the verse (interpretation of the meaning): “but whoever forgives and makes reconciliation, his reward is with Allaah” [al-Shoora 42:40]. Here Allaah states that forgiveness is only good if it is done for the sake of reconciliation; if it leads to bad consequences then it is not good.

Hence the Muslim should look at which serves the greater interest – forgiveness or seeking revenge – and act accordingly. This will vary according to circumstances and the people involved. What Imam Ahmad said about forgiving everyone who causes harm except for an innovator (mubtadi’) is in accordance with this, because he thought that forgiving the followers of bid’ah would have bad consequences, which is that the people would be encouraged to follow innovation. So he stated clearly that innovators were not to be forgiven, as a way of putting people off from those innovations. 

Allaah says (interpretation of the meaning): 

“O you who believe! Whoever from among you turns back from his religion (Islam), Allaah will bring a people whom He will love and they will love Him; humble towards the believers, stern towards the disbelievers, fighting in the way of Allaah, and never fear of the blame of the blamers. That is the Grace of Allaah which He bestows on whom He wills. And Allaah is All‑Sufficient for His creatures’ needs, All‑Knower”

[al-Maa'idah 5:54]

“Muhammad is the Messenger of Allaah. And those who are with him are severe against disbelievers, and merciful among themselves. You see them bowing and falling down prostrate (in prayer), seeking Bounty from Allaah and (His) Good Pleasure. The mark of them (i.e. of their Faith) is on their faces (foreheads) from the traces of prostration (during prayers). This is their description in the Tawraat (Torah). But their description in the Injeel (Gospel) is like a (sown) seed which sends forth its shoot, then makes it strong, and becomes thick and it stands straight on its stem, delighting the sowers, that He may enrage the disbelievers with them. Allaah has promised those among them who believe (i.e. all those who follow Islamic Monotheism, the religion of Prophet Muhammad till the Day of Resurrection) and do righteous good deeds, forgiveness and a mighty reward (i.e. Paradise)”

[al-Fath 48:29]

So the Muslim has the right to forgive with regard to things that have to do with him, i.e., his personal rights, but he does not have the right to remain silent when the sacred limits of Allaah are transgressed. 

It was narrated that ‘Aa’ishah (may Allaah be pleased with him) said: “The Messenger of Allaah (peace and blessings of Allaah be upon him) was never given the choice between two things but he chose the easier of them, so long as it was not a sin. But if it was a sin he would be the furthest of the people from it. And the Messenger of Allaah (peace and blessings of Allaah be upon him) never took revenge for himself, unless the sacred limits of Allaah were transgressed, then he would take revenge for the sake of Allaah.” 

Narrated by al-Bukhaari, 3367; Muslim, 2327 

Thirdly: 

It is permissible for a Muslim to refrain from taking revenge on a kaafir if the Muslim is in a weak position and is not strong. If he is weak then it is permissible for him not to fight. Allaah forbade the Muslims to fight at the beginning of Islam when they were weak and oppressed. Allaah says (interpretation of the meaning): 

“Truly, Allaah defends those who believe. Verily, Allaah likes not any treacherous ingrate to Allaah [those who disobey Allaah but obey Shaytaan (Satan)]”

[al-Hajj 22:38]

Imam al-Qurtubi said, commenting on this verse: 

It was narrated that this was revealed because of the believers whose numbers had increased in Makkah and they were being persecuted by the kuffaar. After some of them had migrated to Abyssinia, some of the believers in Makkah wanted to fight whomever they could of the kuffaar and to assassinate them, betray them and trick them. So this verse was revealed, in which Allaah promised to defend the believers, and He expressly forbade treachery and betrayal. 

Tafseer al-Qurtubi, 12/67 

But when the Muslims grew stronger after having been weak, Allaah gave the believers permission to fight, as He said: 

“Permission to fight (against disbelievers) is given to those (believers) who are fought against, because they have been wronged; and surely, Allaah is Able to give them (believers) victory”

[al-Hajj 22:39]

Imam al-Qurtubi said, commenting on this verse: 

With regard to the phrase “Permission to fight (against disbelievers) is given to those (believers) who are fought against”. It was said that this is the explanation of the words “Truly, Allaah defends those who believe”, i.e., He wards off the plots of the kuffaar by allowing the Muslims to fight and by granting them victory. It implies that He gave permission to fight to those who were able to fight, as is indicated by the context. Al-Dahhaak said: The companions of the Messenger of Allaah (peace and blessings of Allaah be upon him) asked for permission to fight the kuffaar because they had persecuted them in Makkah, then Allaah revealed the words “Verily, Allaah likes not any treacherous ingrate to Allaah”. But after the Hijrah He revealed the words “Permission to fight (against disbelievers) is given to those (believers) who are fought against, because they have been wronged”, which abrogated everything in the Qur’aan about ignoring them and forgiving them. This is the first verse which was revealed about fighting. Ibn ‘Abbaas and Ibn Jubayr said: It was revealed when the Prophet (peace and blessings of Allaah be upon him) migrated to Madeenah. Al-Nasaa’i and al-Tirmidhi narrated that Ibn ‘Abbaas said: When the Prophet (peace and blessings of Allaah be upon him) was expelled from Makkah, Abu Bakr said, “They have expelled their Prophet, they will surely be destroyed.” Then Allaah revealed the words (interpretation of the meaning): 

“Permission to fight (against disbelievers) is given to those (believers) who are fought against, because they have been wronged; and surely, Allaah is Able to give them (believers) victory”

[al-Hajj 22:39]

Abu Bakr said: “Then I knew that there would be fighting.” 

Classed as saheeh by al-Albaani in Saheeh al-Tirmidhi, 2535 

Tafseer al-Qurtubi, 12/68 

Fourthly: 

The Muslim should give up his rights that a kaafir may have taken if insisting on his rights will result in a greater loss of his rights. 

The scholars mentioned that denouncing an evil action may be haraam if it will lead to a greater evil. 

I’laam al-Muwaqqi’een, 3/4 

Examples of that in the matter under discussion include the following. 

If Muslims live in a land where the majority are kaafirs, if one of the Muslims is mistreated, insulted or beaten by them, and his taking revenge will leave to the kaafirs wreaking vengeance on him and on his Muslim brothers, then it is wise for him to keep quiet, in the hope that this will be in the interests of the Muslims in that land. And he should seek reward for that with the One with Whom no deed, great or small, is ever lost. 

But if he can repay this evil and manifest the honour of Islam and the Muslims without that leading to a greater harm from them, then he must ward off that wrongdoing and show pride in his religion, and humiliate kufr and its people. 

And Allaah knows best.