I completely disagree with this viewpoint and this characterization of what Americans believe. You're conflating support for free speech, with support for things like nazism. Which is just incorrect.
Nobody is starting out by saying "nazis need to be able to post their opinions online". It's just that the way free speech works, it unfortunately covers disgusting things like nazism exactly the same as it covers my own speech. That's the whole point of not letting the government abridge or prohibit speech. Imagine if the government did have those powers, and then decided that it was illegal to discuss LGBT concepts or specific religions.
You can't have it both ways; I'm glad to have free speech because it protects ME (and my family, friends, etc) from being jailed for criticizing the government or having specific beliefs, etc, even if it has the side effect of people being able to post disgusting things online. Censoring discussion doesn't stop people from discussing it in secret, it always gets abused by the government given a long enough timeframe.
The original snippet I replied to from the article was such a holier-than-thou comment, and their country's solution of censoring speech ("good" censorship) didn't even work!