What honestly do you think Twitter's hand in this is? Even with a purely chronological feed, people with "selective" critical thinking skills, inconsistent value systems, and a disrespect of personal liberty will still surround themselves with other such people.
Twitter's only option would be to take a "paradox of intolerance" approach and start banning such activity, but then you are trusting a corporation to make such judgments fairly, rather than just expediently.
And if Twitter disappeared tomorrow, what then? Old-school student protests, picketing, signs/posters/pamphlets, letters in the school newspaper, and "cancel-prof-foo.net" getting thousands of views per day.
Ultimately the problem is that people are too willing to join the dogpile and/or are unwilling to stand in solidarity against the dogpile. Twitter doesn't cancel people; people cancel people.
Edit:
I also want to be very clear that Professor Katz, who accused a radical student group of being a "terrorist organization" was absolutely in the wrong for doing so and in my opinion does deserve to be censured for that statement. And making public statements about "black privilege" is even worse, which frankly leads me to question Professor Negy's moral compass and fitness to be an educator. I fully agree with the assessment that they used their rights to free speech irresponsibly, at best.
But I also think it's completely wrong to dig up an old incident for which they had already been judged and punished. I'm sure that the members of the Black Justice League are strongly opposed to policies that take away the rights of convicted felons, and I'm sure that they all have the critical thinking skills to recognize the parallel here, and I'm also sure that none of them would be interested in admitting such. In my opinion the only correct move by the University here is to dole out wrist slaps on both sides and tell all parties involved to drop it or face further consequences.