I rarely use Twitter myself anymore, but I’ve seen enough screenshots and stories to know that abuse is a serious problem on that network. I would have to disagree that people on Twitter are always arguing about “nothing that means anything at all,” however. Sometimes that might indeed be true, but what might seem meaningless to one person can be very important to another, for entirely legitimate reasons.
Regardless, if someone tweets a hateful remark against an oppressed group, they deserve to be called out on it. Not threatened or targeted for revenge, certainly, but made aware that their words have consequences. Twitter is a public platform, and just because the format encourages people to post before they think doesn’t mean that any potentially harmful thoughts they share should be automatically excused as stream-of-consciousness.