OP: Drop out of it for your health.
I use TweetDeck and have columns set up for each of my interests. I have filters that block tweets containing words like "Bieber" (have nothing against him, just not interested). I only have it set up to show me world news and tweets by people that actually do stuff or are 'influencers' in their respective field relating to my work and interests. I also follow a bot that tweets the top posts from a community news aggregation site (HN). It's 60% links to very interesting articles or important world events. The other 40% contains people sharing their work or whatever, but occasionally you will get otherwise awesome people tweeting witch hunts etcetera, while often on the more correct side of a given issue, it can be very agonising with the lack of objectivity or civility. Since when there is crap it is coming from people and not bots or news organisations, I have prioritised the columns so those without individuals (e.g. bots and organisations that I follow) take precedence due to having a higher signal to noise ratio.
A note on social network hate-sprees / witch hunts: If you trace the tweet trail they are often caused by Huffington Post or Gawker Media. There's different levels of hate and stupidity and I am personally never exposed directly to tweets or retweets from the other sources like 4chan, due to who I follow. I do have a list of game-related people and I think the least intelligent or mature debates come from that group.
An alternative to twitter for OP and others: I also use a site called Feedly that uses a simple technology called RSS that many websites have. It's like following on twitter except you only get the actual content of your favourite websites or blogs, and none of the hyperbole.