(1) Every person shall have the right freely to express and disseminate his opinions in speech, writing and pictures, and to inform himself without hindrance from generally accessible sources. Freedom of the press and freedom of reporting by means of broadcasts and films shall be guaranteed. There shall be no censorship.
(2) These rights shall find their limits in the provisions of general laws, in provisions for the protection of young persons, and in the right to personal honour.
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In theory, it is quite easy to fix the problem: Remove (2) and you are done. In reality, no politician would ever try to do that. "You are against keeping children save?", "You are against honour?" and so on. Still, it would be for the best to remove it ... the government uses it to push every shit they want in regards with censorship - after all, basically everything can be restated to be "for the protection of young persons".
In this case, this is hardly a misunderstanding in values as you argue. Most of the URLs are not political and have very little to do with national socialism.
The maintained list of URLs is sloppy and apparently done with little, if any, public oversight. That raises quite a few red flags. The fact that the German government is trying to intimidate Neocities raises many more red flags.
I think both of these points show that it is an unnecessary and excessive restraint of individual and collective freedom.
The German populace was generally supportive of this censorship in the post-war period to mend the ideological rifts that drove society apart in the early part of the cold war. While views are certainly changing in the "information age," if the German populace changes its views on censorship then it needs only to change its own laws.