I think you need to understand the law that supposed to be enforced here, which is not an infringement on the right to Free Speech:
The law against "Volksverhetzung" (§ 130 StGB) came into being as political consequence of the politicial periods in Germany following World War I, which saw the brith and utter failure of the first democracy on "german" territory and the decent into Nazi rule. When after World War II a new foundation for a democratic (west) Germany was written, it's authors tried to learn from the failures of the past and institued a number of measures to prevent the rise of dicatorship ever from happening again.
First and foremost among them are that the first 20 Articles of the Grundgesetz (our sorta-constitution) may never be removed from canon of laws and so overrule in princliple everything else in the constituion. Infringement into the fundamental rights was to be strictly governed and still is (except when it comes to the protections of Mail, Post and Telecommunication but then again there is no paragon state for that anymore).
The law which might be applicable here (if the State Prosecution determines so) is derived directly from Articles 5 and 18 and by lesser extend Article 20 (4) of our sorta-constitution:
(1) Jeder hat das Recht, seine Meinung in Wort, Schrift und Bild frei zu äußern und zu verbreiten und sich aus allgemein zugänglichen Quellen ungehindert zu unterrichten. Die Pressefreiheit und die Freiheit der Berichterstattung durch Rundfunk und Film werden gewährleistet. Eine Zensur findet nicht statt.
(2) Diese Rechte finden ihre Schranken in den Vorschriften der allgemeinen Gesetze, den gesetzlichen Bestimmungen zum Schutze der Jugend und in dem Recht der persönlichen Ehre.
(3) Kunst und Wissenschaft, Forschung und Lehre sind frei. Die Freiheit der Lehre entbindet nicht von der Treue zur Verfassung.
Translation (as best as I can manage, legal german is nightmarish):
(1) All have right to speak and make public their opinion, in the form of Speech, Text and Image, as well as the right to inform themselves from commonly [not equivalent to publicly] avalible Sources. The Freedom of the Press and the Freedom to Report by broadcast and film is provided. There will be no censorship.
(2) These rights are limited by the directives of common law, the lawful prohibitions for the protection of the youth and in the right to personal honour.
(3) Art and Science, Research and Teaching are free [of government control]. The Freedom of Teaching does not relieve from Loyality to the Constitution."(1) is your basic guarantee of the Freedom of Speech and Freedom of the Press, instructing the state to provide a plattform for publication if private persons choose not to - this is just a basic provision and doesn't overrule the editorial power in the public broadcasting services.
(2) only limites Free Speech and the Freedom of the Press within the norms of western democratic tradtion - opening a lawful way to combat untrue reporting, provisions against public humiliation and undue infringement into privacy. (the whole "protection of the youth"-angle is more controversial mostly because of debates what is considered harmful to "the youth")
(3) is one of those post-Nazi provisions. The government does not give preference to any school of Art, Scientific Inquiry or Teaching, this doesn't affect the governmental work to organize schools and universities. But that liberty doesn't cancel out of the legal obligation most teachers have due to being employees of the state. (German tradition has it that most state servants are employed and cared for by the state for life, in return they have are obligated to act in keeping with the law and policy of their employing branch of government if acting in any official capacity)
Wer die Freiheit der Meinungsäußerung, insbesondere die Pressefreiheit (Artikel 5 Abs. 1), die Lehrfreiheit (Artikel 5 Abs. 3), die Versammlungsfreiheit (Artikel 8), die Vereinigungsfreiheit (Artikel 9), das Brief-, Post- und Fernmeldegeheimnis (Artikel 10), das Eigentum (Artikel 14) oder das Asylrecht (Artikel 16a) zum Kampfe gegen die freiheitliche demokratische Grundordnung mißbraucht, verwirkt diese Grundrechte. Die Verwirkung und ihr Ausmaß werden durch das Bundesverfassungsgericht ausgesprochen.
Translation (as best as I can manage, legal german is nightmare):
"All who misue the Freedom of Speech, essepically that of the Press (Art 5, section 1), of Teaching (Art. 5, section 3), of Assembly (Art. 8), of Association (Art 9), the Protection of Mail, Post and Telecommunication (Art. 10), of Property (Art 14) or the Right to Asylum (Art. 16a) to combat the liberal democratic Foundation of the State, void said rights. The abjugation [of said rights] and it's extend [of said abjugation] have to be made by the Bundesverfassungsgericht [Federal Supreme Court]."This is one of the big post-Nazi provisions. Part of the problem during the twilight years of the Weimar Republic (since the legal name of the state did not chase from 1870 to 1945, historians introduced several names to effectively distinguish between political periods) was that both revolutionist Communists and Nazis were in open and public opposition to the state but misused the legal protections offered by the democracy of Weimar to further their agendas - Nazi assemblies, specifically designed to display their manpower and matrial attitude - part promotion, part intimidation - were protected assemblies. Speeches calling for prominent members of society in opposition to the Nazis were protected speech, as such not able to be used as evidence during trails that procecuted actual crimes being committed.
Hower the bar for the application of this provision in the GG is set pretty high. Our Bundesverfassungsgericht is the highest court and the end of legal chain and is oibligated to make rules that stand final point of the chain of appeal.
The law is supposed to be a legal firewall against the radical (of either stripe) political aggitators in public and are rarely used in court, convictions on grounds of that law is even rarer. Mostly investigations on ground of this law end up being tried as civil cases like Slander. This is usually the case because the prohibitions to the application of the law are pretty step:
For that kind of case to apply it has to be proven beyond a doubt that you would be acting in opposition to the liberal and democratic values laid down in the first 20 Articles of the GG consitently
AND have the intention to replace the current state with another.
Most cases break down with the second requirement, but a lot already do with requirement number one - being against the a certain policy or providing a plattfrom for those that are (say, the application of the Right to Asylum) doesn't constitute (in legal terms) opposition to liberal democracy.
However that doesn't end of the course of legal inquiry, esspecially if - as it often the case with e.g. racist statements - there is still an interest in civil proceedings. Said interest is ussually determined by the course case takes - unless the case is of "particular public interest" (which is a determination the Proscution has to proove to the Court), the prosecutors refer back to the person(s) that filed the original case and then it becomes a civil case in which a court has to make determination whose rights are ranked higher (pretty standard case).
All this however has not kept people to use that law as starting point (which is legally valid because it is easier to go from a more extreme law back down to a "regular" on, instead the other way around) and then using the paperwork for a PR drum.
(In my ten years as an activist (yes I do that too, hence my paradoxical dislike to get political on the internet) I've seen dozens of § 130 StGB-cases being filed, only some were procecuted as such and even then the case had to be air-tight and water-proof.)
That the current case has struck a cord with the Prosecutors is mostly a problem of FB's own design. FB is not a company with high standards of transparancy of it's own practices, and so has been a target of dozens of civilian suits in this year alone. However recent legal developments have destroyed large portions of FB's legal defense (e.g. the Safe Habour ruling) and any ruling coming out of this is a legal headway as how to deal with an international company like it.
