I really think we are looking at the whole "being offended" thing the wrong way. Generally speaking, being offended means that we see something and then have a discomforting experience based on our perceptions of what we saw and then react by either demanding that reality to stop or by lashing out and attacking it. Both responses are based in the same area of the brain that causes the fight or flight response and so no matter how people respond, they are still escalating their own intensity. And once they do this, they are also escalating the environment they are in. Many people will have wonderful explanations for why they are offended and can even make some compelling arguments. But in the end, they are still responding with fight or flight behavior and thus continuing a cycle of reactionary living.
And don't get me wrong: I think having a sense of being offended is what makes us human. I am offended everyday by the parochial mentality of so many people I interact with. I am also offended by the fact that as a culture we make someone's wealth the measurement of their value. And the list could go on and on. But you almost never hear me talking about it. Because there is no reason to. I use these reactions as learning tools to help equip my mind to stay sharp and interact with a world, that by and large, is unaware of itself.
We can retrain ourselves to act in a more emotionally regulated manner though! Aha! You can exercise those demons! Exposure is good but is not always the best place to start. I say that because, like anything else, putting oneself into the same situations with the same mindset is not conducive for promoting flexible behavior.
The first place to start is within. Practice quieting the mind on the whole. It only takes about 15-30 minutes a day to do this. Find a quiet place where you can sit and let the mind just "be" without attaching to thoughts. Sounds easy, right? Nope! In this fast-paced world, quieting the mind is a fairly difficult task. Or like an old friend once said: It is simple, not easy. Once you sit in this quiet place, just sit. That's it. If your mind starts to wonder, bring it back to the present moment. If the mind starts to make impressions about your surroundings, bring it back to the present moment. If you start planning on things you want or need to do later, bring it back to the present moment. If you start to question whether or not it is working, bring it back to the present moment. You are probably starting to see a pattern here: Stay in the present moment. That is literally all you have to do.
Once you have done this for a couple months, you can begin to expose yourself to things that you would normally be offended by. Perhaps watch a news outlet that you have been emotionally opposed to and watch a segment. While you are watching, be aware of how you are forming your thoughts and reactions, cognitive and emotional. Try not to get attached to them, just watch how they ebb and flow. The first few times is usually the hardest. But with practice, you will find that you can watch almost anything without being too attached to your responses.
At this point, you might be asking "why do I need to do this" or "what good will this do"? And my answer is very simple, you don't need to do it. You don't need to do anything I suggest. But I have found learning to not get upset, or at least reducing how much I get upset, allows me to be in better control of myself during more stressful times and handle social situations with more grace than before. It's definitely not acting like you don't have feelings or don't respond to things. It's more like responding with dignity. It also offers the other person the space of having their own dignity, which makes it possible to have civil discourse. What you usually find is that you and the other person have more in common when you can have civil discourse.