I can see some logic in filtering out news that’s tragic but you can’t really do anything about. Have an option just have it tell you the important news. I can also see filtering out news from a search because news isn’t what you are interested in. (This has been a problem with me on Google lately: if I google a person or whatever that has been in the news lately, my entire front page can be about that story, even if I’m there for the general topic.)
I can also see having a place where you go specifically for uplifting news, or having social places where news isn’t welcome (say, an option to separate out news into a separate section on your Facebook newsfeed).
But there is nothing gained by actually filtering out all bad news, even that which can affect you. The news can’t act as the fourth branch in keeping people in power accountable if we tune out anything negative. Sometimes we can do something about it–voting, public pressure, boycotts, protect ourselves, talk with others to figure out solutions, etc.
So, really, your question, as asked, is too complicated to pick any of your black-and-white answers.