Here are some reasons that may talk you down:
* The world, and the US has always gone through periods of chaos. This is not the first time we've seen violence and strife, with assassinated presidents and students mowed down by bullets. What's happening now is not worse than what happened before and somehow we still kept free speech intact.
* While certain speech is hateful, painful, and even somewhat dangerous, stifling it only increases pressure and isolation among those being censored. They become more extreme. Furthermore, they are made to seem dangerous simply by the fact that we are censoring them rather than letting them be. The ACLU used to defend KKK marches, and we derided them for the idiots that they are, but still let them march. Furthermore, there's no way to engage in and work through the mental mistakes these people are making if we don't even let them talk. Lastly, they get a persecution complex and don't trust anything the "other side" says. It makes things worse.
* One of the main reasons these people are getting violent is because they are suffering, in poverty, without jobs, and recognize that something is seriously wrong society. They falsely attribute it to race or communism or some other thing, rather than the greedy corporate oligarchy that only gives the common man scraps. The elite would rather resort to censorship than to actually address the problems that cause these people to be unsatisfied and vulnerable to fascistic propaganda. Free speech is not dangerous in an equitable society.
* similarly to the last point, who will decide what speech is ok and what speech is not? The public? That would be mob mentality without standard. The government? Most politician are greedy and self serving. Corporations like facebook? They are beholden to the dollar. No one can be trusted to fairly choose what is not ok to say.