I'm not entirely sure where neonazis come into play here on the topic of human liberties like freedom of speech. Fascists on the other hand... that's the topic isn't it? By applying an amendment to freedom of speech to prevent or force any speech is authoritarian by definition.
Just so we're clear fascism definition "Fascism (/ˈfæʃɪzəm/) is a form of far-right, authoritarian ultranationalism characterized by dictatorial power, forcible suppression of opposition and strong regimentation of society and of the economy which came to prominence in early 20th-century Europe."
I'd prefer to speak solely on the point of human liberties.
And just so we're clear, you can see the differences of civil rights and human liberties which are naturally inherent to all people. https://www.law.cornell.edu/wex/civil_liberties
"Congress shall make no law" - This is the first Amendment of your Liberties, and regardless of the reasoning, changing them will only trade 1 evil for a worse one.
The way it is now is that all may do as they wish... with lawful consequences unless protected by the your rights and liberties. To be clear what I mean is that if you cause damages and there are victims of the "crime" then you should be held accountable. The problem we are facing today is that so many people have those their integrity as to make some people regret having rights and liberties. But it's a slippery slope, imagine on the far side of the extreme where the fed comes to your home in the middle of the night with guns and cameras in tote and force you to say something against your will. That is inherently against your liberty (freedom of speech), would you give this up because someone else said something you don't like?
In my opinion all media should be completely and totally decentralized... a bit like bitcoin. What this means is that no one should be able to control media... not even the federal institutions (especially not them). Fascists and neonazis... well they can all be ousted on decentralized networks for all I care. Every news/media/message should be accountable, but should not be controlled. If someone claims or says something that causes damages it should be accounted for, but there should be no control over it from any outside force.
In China every website, every video, every message has what can be referred to as an OID, in software these can be used as public universal identifiers and can be traced back to a source. The problem with China is that their fascist federal institution will reward and pay people to report and take down any media they don't like. That's fascism. That's the exact opposite of what America should be by our constitutional rights and our inherent liberties. However! Their tracking system is astounding and could help the people take lawful retribution on any damages caused by some created content.
Twitter and Facebook have recently gone to court because of their blatant censorship, editing, and banning or speakers for having differing opinions. They are no longer a distributed publishing houses free. They are now editors and are to be held accountable for their actions and the actions of others on their sites.
I believe that if we add one limit to the liberty of speech and we'll have thrown the baby out with the bath water.