Just as a heads up: I don't have a good working theory here, all I can tell you is what I do myself.
As a former journalist and current PhD-candidate in media studies, keeping up with the news is part of my daily routine. I spend the first half hour to an hour of every morning reading up on things I've missed. And as you know, most news isn't good news. My feed is exceedingly likely to be filled with stories of corruption, disaster and destruction.
What this does to your mood depends on your personality. I personally don't find it particularly difficult to keep my distance and not let bad news affect my spirits, perhaps because reading the news and then doing something constructive with it has been part of my day for so long that I don't stop to think about it anymore. Call it desensitisation, if you will.
But it's also something else. Despite knowing that most of what I'll read today isn't going to be pleasant, I do it because I want to know what's going on. Choosing to stay uninformed of the bad stuff isn't going to help anyone, and will most likely only give rise to unpleasant surprises later down the road. Staying up-to-date helps me keep track of developing stories and how certain events, disastrous or no, came to be. This, to me, is better than waking up to a bombshell of a terrible news story completely out of the blue.
As a final point: you can't affect most of the stuff that's going on in the world, but sometimes you do come across a story that inspires you to spring into action. Me, being a media guy, I write. So when a friend and I came across the story of an online Egyptian frog deity cult that worships Donald Trump, we wrote an article detailing its rise to fame. It's my way of putting a huge and in some ways quite unpleasant story (Trump's election) into some much-needed perspective, and hopefully entertaining a few people along the way. My point is: you never know what news stories will inspire you to act, and this motivation alone is enough for me to keep reading.
You're probably familiar with one Reinhold Niebuhr's Serenity Prayer. The words are far more famous than the guy ever was:
Grant me the serenity to accept the things I cannot change,
Courage to change the things I can,
And wisdom to know the difference.
I personally find this a bit trite and clichéd, but as far as reading the news goes, it might make some sense. The stories that affect you most, those you discuss with friends down at the pub or turn into personal YouTube comment section vendettas, are the ones you shouldn't force yourself to stop thinking about.