Some forms of speech can be prohibited. For instance, threats against some public figures are criminal.
No, threats against anyone are criminal, not just public figures. But the threats have to be imminent and credible; you can't say "he's a nazi so he must be thinking about killing me" because that's not a credible and imminent threat. It's pure speculation and - often - psychological projection since the people who often claim the nazis are violent are themselves advocates of violence, a la Anti-Racist-Action, One People's Project, etc.
Seems to me that it would be within the strictures of the Constitution to ban the Nazi Party, given its history.
Not according to any version of the US Constitution that I have read, and frankly I am shocked that alleged conservatives on an alleged conservative website could make such statements. The US Constitution clearly states what powers the US government is limited to, and banning political parties because "people don't like them" is not a power granted to the government by the Constitution. That's the "living Constitutional" claptrap that the liberals are always trying to peddle: the Constitutional doesn't mean what it says, but is always evolving to fit the "needs of the day". No thank you. That's not a version of the Constitution that any conservative can support.
"Not according to any version of the US Constitution that I have read, and frankly I am shocked"
Hey, you're locked into the mainstream interpretation, and your mind is not open to the proposition that this may not be the correct interpretation. For so long as you remain so, there's no point in discussing it.