About the only thing you can do when someone says (or retweets) something totally idiotic on Twitter is either unfollow, or, of course, reply. In other words, there is no way to register disapproval without simultaneously calling attention to the very thing you disapprove of.
One of the absolute best features of HN is the downvote button and the way it is implemented. Downvotes are stronger than upvotes, and the downvoted content gets buried. A community that lets anyone join has to work hard to maintain a high standard. Downvotes don't kick people out, but they kick bad content off. Twitter has nothing like this, so the worst content gets the most attention. You can choose who you follow but users get no negative feedback on inappropriate tweets. So the norms shift towards whatever creates engagement, which is often outrage, fear, and strongly negative emotional content, with or without any rational foundation.
If Twitter wants engaging and constructive dialog, they need a way to take out the trash.
Unfortunately, Twitter's problem is that their potential for social good and their potential for revenue may never align. Since they are failing at turning a profit, it is unsurprising that they seem to be giving no consideration whatsoever to social responsibility.