When I was younger, I used to wonder: should I care what people think of me? I saw arguments on both sides of the question. And I still do (though I don't care as much anymore). It's one of those questions that follows us around our whole lives, because there are always going to be people who don't like us very much. But should that bother us? Or does it not matter at all? Should we follow the advice of those pop psychologists who say, "Don't care what people think of you! Just be you! You're amazing, you're fantastic, etc.!" What a surprise that such self-help shallowness has so much commercial success: people like being told they're amazing and beautiful and everyone who criticizes them is wrong. Taken literally, that self-help stuff is nonsense, of course. It's a formula for the self-complacency of the moronic celebrity who tweets out feel-good nuggets of New Age flakiness and gets 100,000 retweets. It's meaningless. But then, to what extent, and when, should you care what people think of you?
First of all, it's important to always remember that most people are not very interpersonally, intrapersonally, or logically intelligent. That's just a fact, evident from daily observations, news articles, internet comments, the fact that the average IQ is 100, etc. As a leftist, I try to see the good in people; but I also try not to delude myself. I wish people were more intelligent, and maybe in a humanely organized society they would be. But, for now, I have to accept that most people, much of the time, aren't terribly insightful in their judgments about others and the world. So, the fact that someone reacts adversely to you is in itself not compelling evidence you've done anything wrong or are a "bad person." They may have completely misunderstood you. They may have a terrible political ideology and hate you because you don't want to see refugees die of thirst in the desert. They may be the awful one; their criticism might be an indication of your moral and intellectual worth.
Personally, like everyone, I've been misjudged and misunderstood too many times to count. Someone might think I acted in a rude way, unaware that the reason I made a mildly rude comment was because a moment earlier they had said something insulting to me, which they weren't intelligent enough to be aware of. I, and probably you, am/are constantly kind both overtly and in ways that are too subtle for most people to notice. And yet I've never been one of the "popular guys." Why not? Doubtless because I'm an introvert (and also have different interests than most). Popular narcissists and assholes are everywhere, as are less-popular kind and intelligent types. It's true with regard to the opposite sex too: assholes and/or bimbos (female or male) may be sought-after while kind and intelligent (semi-)introverts are considered less attractive, perhaps because they're more difficult to identify with. Or because they simply don't project the same "confidence," which is an extraordinarily important part of the equation. So the better people sometimes end up being relatively ignored while the least common denominator is beloved.
In all these cases and contexts, on a fundamental level you shouldn't necessarily care very much what most people think of you (or of others). Their opinion might have no implications with regard to your worth or the truth.
The burden of intelligence is that it's condemned to be misunderstood and rejected by a world of stupidity.
The tricky thing is that judgments of you often do have some legitimacy. Even if you were misunderstood, maybe you acted in a way conducive to misunderstanding. So you should try to avoid that in the future. Maybe you should refrain from acting rudely even in response to someone else's rudeness. Sometimes being an introvert can make you seem aloof or judgmental, so to counteract that you should make an extra effort to be friendly. On a non-moral level, to increase your popularity it's certainly a good idea to break out of your comfort zone and try to act a little as the people around you seem to value. Their overall judgments of you may be superficial or wrong, but it's advisable to make tweaks in your personality here and there.
In general, I guess the only rule of thumb is the cliché that you should be open to others' impressions and judgments but don't take them too seriously. Be smart about it. When it comes to your worth as a person, what matter most are principles, not others' judgments. The Golden Rule matters above all: be kind and compassionate, apply to yourself the standards you apply to others, be self-aware and self-critical. And then other common intuitions: be courageous, tell the truth, be rational, etc. Judgments in and of themselves are virtually meaningless; they acquire value only insofar as they accord with certain principles that have cross-cultural resonance.
What this means is that there's some truth to the cheap self-help wisdom after all. From childhood, we're taught that we should try to make an impact on others, we should want approval, want to be loved, achieve recognition and success; but these in fact are not the deepest values that should guide us. Ben Shapiro, the toxic conservative, has "made an impact" and is beloved by millions, as are many other toxic people, conservative or not. The better goal is that of Socrates and Plato: live according to reason and morality. Don't focus on being loved or popular, except as a side-effect of living rationally, morally, and humanely. It can't be said often enough that popularity, or having loads of friends or lovers, or being "recognized," means nothing, despite the status-fixations of the world we live in. Principles are what matter, not people's opinions of you. Don't get down on yourself for what others think of you, unless you think their (supposed) judgments might have some independent merit and are worth considering. Even then, treat them as an opportunity to grow rather than some sort of objective reflection of your worth.
We tend to think of people like, say, Martin Luther King Jr. as more "valuable" than the rest of us because of how many lives they influenced, how much change they helped inaugurate, and so on. But that's wrong. Even though you should want to make the world a better place and orient your efforts toward that goal, your success at doing so isn't what determines your "value." How many people have been as courageous and dedicated as MLK but have had less success and/or been forgotten? Countless thousands. What should determine their value is what they did, not how much change they brought about or how many lives they influenced (or the presence or absence of fame). They deserve to be celebrated just as much as MLK. I dislike the kind of thinking that laments one's not having been as influential as others. "Mozart changed so many lives, gave the world so much, and what have I done??" I hear this sort of thing sometimes. Yes, Mozart had a particular, unusual talent—just as you might have a particular talent he or others lack(ed). Or you might be admirable in ways he wasn't. "Giving the world so much" isn't the be-all and end-all, in part because it depends to an extraordinary degree on luck. The real test, again, is living in accord with certain principles. That's what you should see when you look in the mirror, and that's what should determine your attitude to yourself. The rest of it, more or less, is ancillary.
It does remain frustrating when your goodness or whatever goes unnoticed—as it usually does. It's easy to become contemptuous. That may even be a reasonable attitude, to some extent. How can you not be a little resentful if you're a good person who is treated badly? Still, we should keep those old principles in mind and keep regulating our behavior by self-imposed laws, to speak as a Kantian. No matter how ridiculous people are, act so you can look at yourself in the mirror with pride, knowing that all else is a show, a play "full of sound and fury, signifying nothing."
That's what I like about Chomsky, his personification of principle. No one in history, surely, embodies adherence to reason and morality more than he does. As I've written elsewhere, he's a useful tool to keep yourself on the right path.