Shooters, unsurprisingly, are traditionally set up around the idea of shooting things. The ability to aim, dodge bullets, and ultimately, kill enemies without being killed are the skills that these games value above all else and in online situations, those who cannot do those things need not apply. For games like Call of Duty, Halo, Battlefront, and others, if you aren't good, you're bad, and if you're bad, you were subject to horrible verbal harassment. Neither the game nor the community could show the weakest newest players any sense of understanding or tenderness. Not only did they lack the encouragement to do so, they also lacked the tools.
In 2007, Team Fortress 2 came out and for one of the first times, there were multiple ways to help win a game. There were quite a few classes of characters shaped around death and destruction, of course, but alongside those, there were the characters who supported them to victory. You had the Medic, Sniper, Spy, Demoman, Heavy, and the Engineer. By breaking down the methods of play into classes, some people would be more offensive, some would defend, and others would have the job of keeping everyone alive. Each one had its value and place on a team. This meant, if you weren't good at the traditional objective of running around killing everyone, there was a job you could do. Medics, largely non-combat units, were needed to keep everyone else alive on the team by sacrificing firepower for the opportunity to back other players up. This was one of the first signs of a developer thinking about shooters in a different way.
Though the shift hasn't been immediate, games like Warframe, Overwatch, Destiny 2, and Splatoon all have non-combat ways to contribute to the team. Every single one of those games has a less toxic community than games like, say, Call of Duty. I don't think this is a coincidence. Having players supporting one and other and having more tools to do so, has had a hand in creating a slightly less toxic communities in these games. If someone doesn't aim well, having another option to play a character that can heal or back up a better and more experienced player, creates a situation where the inexperienced player isn't automatically considered trash.
Destiny 2 and Splatoon 2 are games which I believe demonstrate this idea quite well. In Splatoon 2, the community is, actually, rather positive. Primarily because, as long as players are doing their best to put ink down on the map, they are doing everything they need to be doing. Quite contrary to most games, the Splatoon community values players who focus on non-combat tasks vs the person who shoots moving targets the best. This shift of focus off the performance of individual players means that people spend less time miffed at a particular person on their team. In Destiny 2, Warlocks and Titans are able to support their teammates with shields and healing circles. And every player has the ability to revive other players whenever possible. If someone isn't great at aiming but, they try really hard to revive their team members when they die, it's much more difficult to get angry at someone in Destiny 2.
Ultimately, toxicity isn't good for anyone. The people being toxic are toxic because they are frustrated, the people who are targets, obviously suffer, and everyone else has their entire game feel less fun. To counteract this urge to be a jerk shooters, especially, need to offer players more opportunities to practice kindness instead of anger.