I suspect most cases are like mine, not misunderstanding so much as encountering an exception to the default "safe" set of assumptions. When someone maligns a political party or institution it is usually partisan, emotional, and unfair. When encountering this, in the vast majority of cases the official position will be quite close to the "real" one. AfD secretly harboring a significant number of actual bonafide nazis in high ranking positions and actively covering this up is very much the exception the world over.

If you seek to convince people then leading with the sort of examples you linked me is probably the way to go. For those open to new information it cuts to the chase and the rest you weren't going to convince regardless.

The trouble with the german approach that bans political parties is IMO that it creates an easily abused tool that muddies the water. It's no longer so simple to judge a given situation since now you need to consider the content and context of the speech as opposed to merely whether or not it constituted a direct threat of violence.

Meanwhile I don't think it's likely to be effective for the stated purpose. In one scenario the extremists get laughed out of the room as a tiny minority. In another they hold the majority in which case banning them is extremely unlikely to work out favorably. Imagine if Trump who won the popular vote this last time around had been banned by the sitting establishment. There's no way we come out of that unscathed.