Yet many of the German Nazis still have those at home, they can be shown in educational contexts or in museums etc. Forbidding something doesn't make it go away, it just shows where the free democratic society you live in draws the border.
Germany has been a democracy before the Nazis took over in the 20s and it is one again today. However many Germans are well aware that this could change again in the future. You might have heard about the paradoxon of intolerance: if you are tolerant to fascists, because tolerance is your highest value, one day they might come to power and create an intolerant society — therefor if maintaining a tolerant society is our goal we paradoxically have to show intolerance to those who want to abolish it.
This means Germans weigh the value of our democracy surviving fascist uprising higher than even freedom of speech.
But when you say "vibrant right wing" and they're "just...not allowed to display Nazi insignia", are you referring to the extreme right wing that're basically Nazis without the logos?
If so, given that they exist, what do you see as the point at all of having those bans on the iconography? It seems your society largely _does_ have the mental defenses that I agree with OP are necessary to combat the downsides of free speech writ large. So then why have those bans in place at all?