Ben Shapiro is not a white supremicist. He is a conservative podcast host like a Shawn Hannity type. His arguments are more well informed and crafted than Shawn or most conservative radio show guys, but his wordchoice can be kitschy, unapologetic, and beligerant. He likely does it on purpose because he scores points with his core audience and it gets people talking about him. He wasn't banned from Cal, but nearly 1,000 people came to a protest, I believe antifa tried to prevent him from coming, and the only reason it didn't get violent was probably the huge police force that was ready for the protest. Nine people were arrested though.  http://www.latimes.com/local/california/la-me-berkeley-protest-shapiro-20170914-htmlstory.html

The reason the police were ready was probably because of the rise of violent protests on campuses. I can't find it right now, but I watched a video of a man throwing a chair at people trying to walk into a speach at one university. Here is a list of a few violent protests, one of which was at Cal, not sure who the speaker is, so I can't speak for whether he is a white supremecist. http://www.foxnews.com/us/2017/04/21/violent-or-disruptive-protests-on-college-campuses-in-2017.html.

Here is Shapiro's visit to Utah. http://utahstories.com/2017/09/university-utah-protest-ben-shapiro-nearly-turns-violent/