The fallacy of this comment is the word "violently."
Although I count myself as a "lefty" I actually agree that the left has a problem with political correctness, thought crime, whatever you want to call it. To the extent that we promote certain world views (e.g. "Black people are not an inferior race") we should do so with then intention of persuading people who disagree with us, not cowing them into submission. There needs to be a safe space for conversations about sensitive topics, and for people to be able to talk and reason through viewpoints without fear of reprisal.
There is a time and a place for such discussions. For example, it might be appropriate for me to debate racism with my close friend in private. It would not be appropriate for me to say hateful things about black people in front of, say, my boss or a kindergarten class. Twitter has decided that they don't want to be a forum of these types of discussions, and they have every right to moderate the kind of discussion that takes place on their platform.
Twitter isn't censoring David Duke with "violence." He is not being arrested and put in jail. Twitter is just saying, hey, this isn't the kind of platform we are, we're worried that your hateful comments are going to drive away users and impact revenue, go promote your hate speech somewhere else.