The usual defense I hear for the laws is that they don't like neoi-nazis and prefer to keep the neo-nazi propaganda illegal.
The relevant paragraphs restrict a lot more than Nazi propaganda. And, sure, as long as you accept the German dogma that those laws are compatible with democracy and free speech, that they simply represent a different and possibly better choice, people are happy. Suggest that current German law is in anything other than a model of democracy and they get mean.
America is a bad example since you have as many if not more extreme right wingers than Germnay.
Based on what? Given that extreme right wingers can't even legally voice their opinions in Germany, how would you even know? Keep in mind that the hotbed of neo-Nazis in Germany is the former East Germany, a part of the country where any right wing tendencies used to be harshly punished.
It is not illegal for them to be extreme right wing, just holocaust denial and use of nazi symbols outside historical contexts. They do have over-ground political organization and demonstrations. The main thing keeping them somewhat underground is not the law, it is left-wingers trying to kill them. If there is a neo-nazi demonstration of 10,000, 50,000 anti-nazis show up to kick their ass, and the police ends up spending more resources protecting them and oppressing them as you seem to have the impresion they do.