Generally I am a fairly optimistic person and I see the best in others. There are few things that make me lose my faith in humanity, but petty, small-minded bigotry is one of those things.*
I am far from perfect, and have my own moments of prejudice, fear, and hatred. After all, I have simmered in the broth of our misogynistic, racist, xenophobic society my entire life, so it is no wonder that some of it seeped into my mind. But I have an innate, very strong sense of fairness that I employ at every opportunity, which helps free my mind of biases.
I told my sister once that what made me a good mathematician was that I was fair with the numbers. When I come up with a candidate algorithm in my work, for example, I try to examine it from as many angles as I can, both the general case and as many exceptional cases as I can muster. In this way, I can further refine the algorithm when I find an exception, or verify when that it will work.
I employ the same technique in my day-to-day dealings with people. Sometimes, people do things to me that I perceive as being (for lack of a better term) really shitty. The easiest and most direct explanation for why they may have done that is to attribute it to pure mean-spiritedness on their part. This is a very simple and elegant explanation -- it requires no creativity or originality, it aligns with my angry feelings about the situation -- but it is also completely false in the vast majority of situations.
No, the vast majority of people are not cruel. They're just regular people like me -- people who make mistakes, who don't have all the information they need to make the optimal decision, who have unexamined biases. They've been hurt in life, and have buttons that other people can inadvertently push without meaning to, just like me.
Dehumanizing your enemy -- making them out to be inhuman monsters -- is deceptively cheap, but costs more in the long term. It also leaves you powerless against this inhuman onslaught of cruelty. There is no connection to which you can appeal for decency. There is no way to stop the evil without escalating it to the next level. This in turn begets more cruelty and suffering, and the cycle continues.
I recently learned of a situation in which I was the target of a great deal of derision and mockery. That, friends, is my button right there, installed by my upbringing. My first reaction was to recoil in horror at the cruel junior-highschoolers in adult bodies who were made entirely of pure evil. But soon I was able to bounce back from the visceral fear I felt because of the situation, and consider the motivations of those people who were so hurt that they had to hurt others to feel better about themselves. I thought of the times that I had mocked others, even though I have never gone to the extreme levels of derision that these individuals did. We all have our moments of terrible insecurity.
Then I thought about how I could approach this situation with these individuals. What do we have in common? Where can I make a connection, and diffuse this tense situation? I think I know the answer to that. And while they may be so hurt that they can't take the hand that I'm extending, I'm okay with that. The important thing is to maintain my humanity along with my dignity when facing these adverse situations.
* This is not to say that there is such a thing as profound, open-minded bigotry.