Protesting electoral fraud is also absolutely required, even if I am extremely extremely sceptical that it actually happened.
Some of the protests that happened in the civil rights movement were indeed violent although this has been rather aggressively whitewashed in government approved public school classes meant to teach students the way to affect real change is to stand around with signs and sing songs and have racist white police officers beat you until you win (Kings flirting with communism and advocacy of reparations doesn't get much mention either). Ever hear of this guy called Malcolm X who wrote quite a bit about violence, he's definitely not somebody who could be allowed on social media. Race riots happened, people got beaten, some were killed largely by the police (just like in this most recent protest) but also by protesters (just like in this most recent protest). Did this delegitimize the civil rights movement? No, it was a noble movement, people just whitewash and dramatize it instead to prevent any degree of cognitive dissonance, and then compare modern day movements to the whitewashing to whitewash the modern day equivalents.
Back then like today, the degree of violence was greatly exaggerated, disproportionately by the media and by racist segregationist's. Protests are mostly a dull affair filled overwhelmingly with non-violent people and only the exciting bits hit the front pages. The extent of violence by Trump supporters too is greatly exaggerated, mostly by media and their political opponents. If one police officer dies and 4 protestors, the only reasonable reaction is a speech crackdown against those who blame this incident on democrats dubiously. Since obviously cracking down on the free non-violent exchange of ideas and advocacy of peaceful protest is what prevents violence from happening.
Point I'm driving at is that if the entire argument is based around the idea that any violence, or even violent mobs, delegitimizes a large movement than virtually all movements from BLM to the Civil rights movements to... whatever this is.... are delegitimized. Really the issue people have with the Trump supporters, above all, is that they're wrong and unpopular. As such they're a good test for exactly how much people REALLY support freedom of speech and the right to protest a cause that isn't broadly supported.