I only know because I'm reading a book about it now. A frat house had a charity event called "The Ugly Man Contest" that was won by an obscene entry. Soon thereafter a kid was on Sproul Plaza (the main public plaza where a lot of the action takes place) with a piece of paper with the F word written on it. A passing police car drove by, and since this could be seen by any pedestrian on the street, he called it in to campus police, and the kid was arrested under obscenity laws.
The Free Speech Movement had essentially won at that point (having used a lot of direct action tactics similar to BLM). However a couple of the FSM leaders thought it was an injustice that a lower class kid would get arrested for his social protest over the F word while everyone looks the other way when Frat kids break obscenity laws. When they couldn't get anywhere through proper channels, they threatened to hold an "Obscenity Rally". The administrators tried to warn them that if they did they would be giving away all the gains of the Free Speech Movement to reactionaries.
The next day they held a rally that included cheers, plays, literatures, an edition of SPIDER magazine with the F word on the cover, and just about everything you can imagine dealing with the F word. The Young Republicans (who were part of the FSM United Front Alliance) ordered "F- Communism" T-shirts.
There was a conservative backlash among certain faculty on campus who had already been furiously writing editorials and appealing to their friends in the State Legislature about what allowing political advocacy on campus (what FSM was all about) had led to in terms of the decline of education and morals. This even included a letter of inquiry regarding birth control policies on other campuses! Quel horreur!
The Regents of the University of California were on the phone in no time demanding expulsions over all the "moral license" and "degradation" on campus. The President of the UC system was outraged at the interference but also angry that the FSM had pushed things this far. He handed in his resignation. There was some bureaucratic theater which resulted in the faculty begging him to keep his job and ultimately launching inquiries and reports that rolled back the FSM. Reagan came a year later claiming that something had to be done about those kids at Berkeley where he could point to the Filthy Speech Movement as an example of how bad things had gotten.
Sadly, if you look at it as a class issue and a Constitutional law issue, the kids were right.
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