Chomsky defines his ideas of the limits in his previous quote.

If we don't believe in freedom of expression for people we despise, we don't believe in it at all."

But the context of the larger quote is referring to antifa specifically, so whatever his views on the limitation of speech, he thinks antifa is disrespecting the "fundamental principles of freedom of speech." 

Chomsky's thoughts are clear and much more consistent with anarchism and libertarianism than antifa's.

Chomsky may be fine with people talking about killing blacks, Muslims, gays and Jews, but I'm sure as hell am not. Also, why would you not want to be anti-fascist, when fascism is such an authoritarian ideology? Wouldn't you want to oppose it?

False equivalency. Not using violence against activity does not mean you are fine with it. 

I am anti-fascist, obviously. As are most people in the world today. But I don't think ends justify means. I am principled in my belief in the equal application of liberty, and that includes for people with views I don't like. Otherwise, I am giving the nazis and fascists precedent to do the same to me. As I said before, most of the people antifa protest and label as fascists or nazis are not fascists or nazis. 

That's a huge problem, though. They don't need precedent. They're ideology is inherently violent, so they view their violent tactics as just, much in the same way that I see a violent revolution as just if it leads to a socialist society where people's needs are met and where cooperation replaces competition as the main economic goal. Ideally, violence wouldn't be needed: social ostracization would be the ideal solution. However, I highly doubt that they're going to promote something like peaceful genocide or peacful ethnic cleansing or even "peaceful authortarianism", and I don't trust them to give me freedom of speech, because they view socialist, anarchist and communist views as a threat to them.

Can you name a person or group of people antifa has protested whom call for genocide, ethnic cleansing, etc?

But even if they were, we are talking about legal precedent and moral precedent in the eyes of non-fascists, not the fasvists themselves. I am talking about the apolitical, moderates, etc. If antifa gets away with violence aimed towards fascists, then people will be numb when fascists do the same to communists. 

I suppose the gap is too wide, but I view violent revolutionary activity as having been mostly unsuccessful. Working outside the state and defending oneself when attacked by it are okay. But actively trying to violently overthrow it never ends in a truly free society. Just despotism. Also just waiting for the proleteriat revolution is lazy in my eyes, especially in a petite-bourgious society like the U.S. If all the people who are ready to use violence instead aimed to create mutual aid societies and strong trade unions (per Kroptopkin) socialism would be a reality for many. Instead they'd rather burn trash cans, throw molokov cocktails, destroy personal property, pepper spray bystanders, and exaggerate about genocides which are not going to happen in today's developed world. 

Also socialists and fascists fought like this in Italy. Mussolini won.

I'm not a part of Anti-fa, but I'm pretty sure they oppose Richard Spencer, who is a white supremacist that supports black genocide:

https://pbs.twimg.com/media/C2s9KqZUoAAwtXU.jpg

Also, you're talking about people being numb to communists being killed, which would gloss over that it already exists: the American military is bombing and killing thousands of people, yet the public are generally apathetic towards it.

They oppose Richard Spencer, yes, but Richard Spencer is not the guy speaking at these events where hundreds to thousands of antifa come and shut down. One guy punched Richard Spencer as he was interviewed, that is it. And honestly if we are going to cite Richard Spencer in order to make the case there is a realizable and flourishing fascist movement in the U.S then we are bending backwards looking for it. Richard Spencer is as niche as it gets, and if he does have beliefs in genocide he knows well to hide them when interviewed. Not to mention that the American polirical system allows for a lot of subsidarity and separation of powers. Something Trump discovered quite quickly. There is no legitimate threat of fascism in the United States, and the people antifa are protesting were not calling for violence, unlike antifa. 

The U.S military is bombing and killing people abroad. If people are getting attacked domestically, Americans care much more. If it can be shown that these people deserve it somehow (say they belong to a gang) the Americans grow callous. If antifa uses violence, and the hard right respond in kind, Americans are going to think that both groups deserve it. Right now Americans think all people should have absolute free-speech, including communists and fascists. But if we limit one extreme ideology or allow for its limitation, why not the other to be fair? Which was Chomsky's point on tactics.

So you associate yourself with the group that initiated violence in Berkeley?

The OP posted it as an either or, and I sure as hell am not going to side with Anticom! That would be entirely counterproductive. In reality, I'm an anti-fascist that doesn't belong to any group, so my views and actions aren't necessarily indicative of Antifaschistische Aktion, and vice versa. However, if you read their hsitory they originated in the 1930s to oppose Nazi Germany, which is a good thing I'd say. Whether or not the people in the Berkeley riots were even a part of Antifa, I don't know.

They label themselves as Antifa and from what I am seeing their purpose on that day was to use violence to stop a rally about free speech.