Should Colleges Fire Their Communists?

At Crooked Timber University of Bristol professor Chris Bertram defends laws against "hate speech?" He writes that speech can indeed cause harm because "being bombarded with the message that you are of lesser worth than others, are disgusting, repellent, vicious or stupid, may well cause you significant harms (and where genocidal crimes have taken place, it is often against the background of such messages being prevalent). "

Well, over the last 100 years the type of speech that has most often resulted in harm is speech advocating communism. And, many "genocidal crimes have taken place" in the background of pro-communist speech.

So my question for Chris Bertram is, should Western governments ban pro-communist speech and should colleges fire their many communist professors?