Feeling offence, resentment, bearing a grudge are emotions many living creatures experience, not only humans. Such feelings can be directed towards particular people, against the groups, institutions, society as a whole, a situation as such, etc., and can have no particular object but be manifested as a general feeling. The problem is often exacerbated by directing of a reactive action not necessarily against the real cause of dissatisfaction, but to a foreign to this cause entity. It might stimulate revenge, retaliation and other actions, which are non-productive and destructive, and not only for victims, but, as a rule of thumb, for both sides, and exceptions are rare. The possible consequences of this emotion could be huge, up to the ruining lives or causing deaths, with the overwhelming spectrum lying in the range of substantial and serious troubles. Thus, those willing to reduce the impact of this (really troubling!) emotion on theirs lives should acquire and consistently train certain skills and perceptions. One can think of these suggestions as mere tricks, if he/she does not agree with theirs underlying ideas. The important thing is that these tricks work and solve real and all too often encountered problems, but not theirs "ideological" foundations.
The most important skill is to not feel as being offended. First we should think what are the reasons causing this feeling. True, there could be many of them. In my view, the main underlying one is that we either equate ourselves with the offending party (and so expect from them predictable and fair actions), or give too many credits to the offender, like rational thinking, knowledge, calculated intentions, sophisticated plans to offend namely us, etc. In 99.9% such assumptions have absolutely no grounds. People are different, that's true, the spectrum is enormous, from wise and clever people like Anaximander and Aristotle to stupid animals with human appearance, barely comprehending few tens of words, if any. However, the majority, those 99.9% act exactly like all animals do, on instincts only, using formal reasoning merely for justification of their instinctive actions. (We, humans, at the first place are animals, but not the rational creatures - keep that always in mind.) Feeling offence inflicted by those animals, is it rational? One would be unlikely offended by a barking dog, because the dog cannot be accounted for that, it knows no feeling and notion of responsibility. However, this situation is 100% transferable to interactions with the overwhelming majority of people, who also have the same level of responsibility and accountability, and sometimes about the same intelligence. We should not expect from people what they cannot deliver in principle; they just don't have such abilities we too often expect from them, for no reasons other than false stereotypes.
The cause of such an inadequate attitude is that we were raised in this way, by parents and educational system, with unrealistic expectations and wrong ideas of what a human society is really about. Why society does such a bad thing to us? There is no simple answer to this question. Among the main reasons is that governments and powers want us to behave in a convenient for them way, which first of all includes obedience and compliance with rules and laws introduced by powers. Parents also prefer children listening and obedient to them, since they (in a long run - wrongly) think that such a behavior will give them less troubles, and will be more beneficial for their children - now and in the future, which is a erroneous assumption, because obedient people are used by other people and governments as tools, resources for theirs good, in detriment to lives of those obedient people.
So, we should get rid of unrealistic expectations and ideas about the people around and societies we leave in, in order to not feel offended by their actions - they just cannot act in a different way, as a dog cannot stop barking (unless it is forced). Such a vision implicitly includes an idea of dividing people into groups. The smallest one - in fact, of a miniscule size - are people who can exercise reasoning, feel measure and have a socially sensitive and responsible mindset. However, normal people do not have problem with representatives of this rarely encountered group. For the rest, we should view them at their real value, understanding that they on animal instincts but not any kind of rational thinking. Once our imagination does not assign them intellect and reasoning abilities they do not have in principle, we cannot be offended by their actions.
The next important skill in dealing with offences and grudges is to intercept these feelings. This means realizing right away that we feel offended. For that, we should train mindfulness, which is a state of mind monitoring our thoughts almost at a subconscious level, that is of what kind our thoughts are; either they are productive, constructive, wholesome, or the opposite is true. If our thoughts are destructive, unwholesome, we should immediately relinquish them, using certain technical tricks, like thought replacement, switching to good thought, etc. (see Mindfulness courses, books, there is plenty of material on this topic, and some is really good). Thoughts that we are offended by are non-constructive ones; in fact, they are destructive, turn off our thinking abilities and reasoning - the best ground for making mistakes and creating all sorts of problems for ourselves. Feeling being offended should be considered as a red alert of the highest degree - there is a very serious abnormality with our state of mind! It needs extraordinary attention and immediate curing efforts.
Abstracting and separating our minds from the others and the environment. This is a somewhat subtle skill and perception to develop. Until I trained myself to get to this state of mind (and I am certainly not an expert in this but rather a novice), I did not think that it is possible at all. In such a state, I feel indifferent to what happens outside. It's like I erect a transparent but impenetrable wall between myself and the rest of the world. What happens there is not my concern; I have no means to influence the situation there, nor do I want to. My resources are limited, I must use them to serve my needs. Others should serve theirs needs. They have the right to have their own opinion and perform their own actions. However, with this right comes full responsibility for their actions. If theirs action offends me, that is my problem that I took it so personally. It is their right to do such things, but I do have no lesser right to act in my way and ignore their actions and intentions.
Another explanation could be that I abstract people and situations to the outside space from my mind and my sphere of interests and immediate actions. Here is my life space. There - theirs. And we do not intersect. Now or forever, we'll see.
Consider calmness of mind as a necessary feature and quality in everyday life. Feeling of offence introduces agitated state of mind, disturbs and jeopardizes our thinking abilities and through this - creates problems. We should intercept any deviation from a calm state of mind, put aside everything else and start working on returning calmness of mind. Technical means are many, like breathing ("square"), meditation. I formulate this important principle as "Not calm - STOP!" Take no actions and decisions in agitated state of mind (which feelings of offence and grudge also always create).
Summarizing the said above.
We should not think about people what they do not deserve and do not possess. Overwhelming majority of people are simple and primitive creatures we should expect little from, if any.
Develop ability to always monitor your state of mind.
Intercept bad emotions and state of mind in general, and propel the good ones.
We should mentally separate, abstract our personal living space from disturbing our mind people and environments, do not allow those strangers reside in this space. Being too connected (to other people and anything else) is not a good thing. Dependency shapes our minds and actions. Almost always, dependency works against us, against our interests and needs, sucks our resources, which otherwise could be used for ourselves.