TL;DR: Answering toxicity with positivity and kindness will go a long way to improving your Overwatch experience.

With the amount of toxicity in Overwatch, and indeed the greater competitive gaming world, I wanted to take a moment to highlight what I consider the best way to deal with it and to maintain a positive gaming environment. If you have played competitive mode for any reasonable amount time, you have likely seen some toxic behavior, regardless of your SR. The worst thing you can do is let it spread to you.

Humans have a natural tendency to be mirrors for each other. When interacting with someone, we tend to mirror our reactions and attitude based on how we are approached. When someone is polite and respectful, we are more likely to respond positively, whereas when someone is toxic and hateful, we are more likely to get upset and respond in kind. This is called 'Complementary Behavior', and is the most natural way to respond to a social situation. It's not any kind of personality disorder if you are approached with toxicity and devolve to the same level, it is just basic human nature. In this particular environment, we leave such an interaction with flared temper and hot head, and bring that with us to the next game. That is how toxicity spreads so virulently in games like Overwatch where games are rapidly queued back to back with very little down-time during which to cool our heads.

However, there is a way to break the cycle by upsetting the mirror environment. It is called 'Non-Complementary Behavior', which is far more difficult because it is like grinding gears of our natural psychology. When someone approaches you with toxicity, if you respond with kindness and respect, they have suddenly had a wrench thrown in their expectations. Like they have looked in a mirror and seen something different than they expect looking back at them. It can play out in a few different ways, but all of them have a much more positive outcome than if you were to respond with as much toxicity as you receive. Here are some scenarios that I have paraphrased from actual Overwatch encounters.

Situation 1: You have just had a rough game on Numbani where the opposition completed the map, and your team didn't even capture the payload. Someone on the other team is exceptionally proud of themselves and calls you out specifically, "GG EZ, I wrecked you, D.Va! You are such trash!" You check and it's a Reaper that killed you several times and really stood out as the biggest threat on their team. Rather than mirroring him and sending insults his way, you say, "Yeah, you got me pretty good! XD Well played!" His response, "Dang, trying to troll here. Touche. Good luck next game!" In this situation, a hostile approach was answered with compliments, which caused his own attitude to change into something far more positive. This is an extreme example, but one that brightens my day beyond comparison when it happens. Most often the toxic behavior just stops or is calmed down to a more reasonable level rather than doing a complete 180. It is hard for people to continue to be toxic in the face of such positivity, but there are of course exceptions. See further situations below.

Situation 2: King's Row, your team almost got the payload to the end, but an ill-timed ult caused you to lose the final team fight. There is still another round to play. Your mercy is livid and going off in voice on you about your misplaced ult, even though you have otherwise been playing well the rest of the game. You respond with, "Yeah, that was my bad, but your healing was great. I think we can hold them at first point easy." Your Mercy doesn't have any shift in attitude, posting in all-chat, "Report our Zarya for throwing." They may be too unstable to change their attitude in the heat of the moment, but this can still have a positive outcome. You also post in chat, "GR :) Nice shutdown, Zen," referring to the Zenyatta on the other team whose own ult nullified yours and won them the last fight. With this, both teams have seen positivity from you, and negativity from your Mercy, which as a result makes it abundantly clear that Mercy is in the wrong. The other team comes to your defense, saying that you are doing very well and clearly not throwing, and your team verbally praises your well-timed shields. You may not have shifted the Mercy's attitude, but when you are presented with hate and hostility and respond with kindness and positivity, you make it clear to everyone watching that the other person is the asshole.

Situation 3: You just had a Nepal game where everything went wrong that possibly could. Your healers switch to DPS without saying anything, the enemy team practically held you at spawn the whole game, and everyone spends the game blaming everyone else. When you get a moment to put a word in, you say, "It's ok, we had an off-game, that's all. Next game will be better." But nobody comes around. The environment is too charged, tempers too hot, and blame and insults continue to fly. There are some situations where you can't change the attitude of other people, but it's ok because you have still accomplished something: You have not devolved to the same level of toxicity. You have kept things positive, which makes it easier for you to shrug off this loss and move on to the next game. You post in all-chat, "Well played, you guys trounced us! Nice job :)" If you can't get a positive word from your own team, at least you are letting the other team know that someone on your team can keep a positive attitude even in the face of such harsh defeat. And that at least makes a small part of the community a little better.

I have seen plenty of tip lists for ranking up, and among them very frequently is 'keeping a positive attitude'. I rolled my eyes at first, but they are not kidding. Keeping a positive attitude and spreading that to others really does help win games and improve your overall experience with the people that play with you. Keeping things positive from the start can prevent toxic behavior from taking root to begin with. This isn't a perfect system. Not everyone will respond the way you want them to, but by not mirroring the toxicity you are preventing it from spreading, and if nothing else, you will make your own experience a more positive one as a result.

More on Non-Complementary Behavior