Sure there are absolutely some issues from social media that are worth highlighting in the news media, but all shit storms and online controversies aren't created equally. To often one or two posts are taken out of context, especially on Twitter where people try to cram their message into as few words as possible. That is then elevated to "This person is horrible" or "All people in this group are bad".

The reality is that some people are just assholes, and while annoying and terrible, it's simply not worth writing about.

We would need to convince people in society that it's not "worth writing about", which isn't going to happen. It's radical information freedom. People get access to information they would never have had access to previously. A drawback of that is that people become free to act on information they would never have had access to previously.

The thing about Twitter, (about most social media actually), is that they are built on the reality that the vast majority of the population believe this stuff is, indeed, "worth writing about". That's how they make their money. Everyone writing about what everyone else wrote about. Business is good precisely because everyone thinks all this stuff is "worth writing about". And there is no sign anyone will meaningfully change.

I don't see much hope actually. My best advice is try to maintain your privacy. (Well, I guess also "don't be an asshole" is pretty good advice as you intimate.)