There have been a couple different high profile incidents involving protesting (some of which escalated past normal protesting) in order to get certain speakers cancelled and disinvited from booked events.
Safety concerns stop performance by Milo Yiannopoulos, guest of Berkeley College Republicans
news.berkeley.edu
As conservative radio host Ben Shapiro spoke at the University of California Berkeley, protesters swarmed outside chanting various slogans.
www.wral.com
If Berkeley doesn't want to be "unfairly labelled" as the "woke school"...
Perhaps things like "Disinviting Bill Maher, because he said something mean about Islam on HBO", and "riots with a $100k worth of damage and banned weapons being brought on campus by protestors because Milo was invited to speak", and "phoning in bomb threats to prevent Ann Coulter from speaking", and "Ben Shapiro needing to be protected by 300 cops just to get him to the venue because protestors were trying to block it" is the sort of thing they'd want to curtail a bit.
When you boil that down, it's basically like saying:
"We're not
woke, we just have a large subset of people who throw temper tantrums, light stuff on fire, and phone in bomb threats when the college republican group on our campus invites people to speak who we feel triggered by"
And that "bad look" is made even worse when, for a few of those, faculty actually participated in the protesting outside the venues.
The professors should've been the first ones volunteering to go up to mic to take on Shapiro head-on during the hour long "open mic" portion of his events, not screeching out in the parking lot with some of the students.
PR is 90% of the game with regards to perception.