Was Mark Twain's book 'The Adventures of Huckleberry Finn' banned in the former German Democratic Republic (East Germany)?

No. It wasn't "banned".

And, well, yes. It was an examplary piece of world literature. Not to be ignored.

Indeed: Much well liked by the governmental censors. But the very word "censors" brings up the problem. It was a bit shortened — for anti-authoritarian tendencies — and sometimes a bit strangely translated.

One thing was that Huck was seen as a potentially problematic role-model for the youth (which he clearly is, in many authoritarian eyes. Going about stealing stuff was seen as a problem…). This was as a tendency cut short, ad usum delphini.

Then we had an early example of 'politically correct language'. Examplified in the translation choices. Especially in the character of Jim a certain coloured language was tried to be avoided, to different degrees in different editions.

For example in the edition published in 1963 GDR we find the following passage, shown here first in the original, then the published GDR-German translation and an attempt to re-translate that back into English:

Original:

»What do dey stan’ for? I’se gwyne to tell you. When I got all wore out wid work, en wid de callin’ for you, en went to sleep, my heart wuz mos’ broke bekase you wuz los’, en I didn’ k’yer no’ mo’ what become er me en de raf’. En when I wake up en fine you back agin, all safe en soun’, de tears come, en I could a got down on my knees en kiss yo’ foot, I’s so thankful. En all you wuz thinkin’ ‘bout wuz how you could make a fool uv ole Jim wid a lie. Dat truck dah is TRASH; en trash is what people is dat puts dirt on de head er dey fren’s en makes ‘em ashamed.«
Then he got up slow and walked to the wigwam, and went in there without saying anything but that. But that was enough. It made me feel so mean I could almost kissed HIS foot to get him to take it back.

German GDR version 1963:

»Was die bedeuten? Ich werd’s dir sagen. Als ich von der Arbeit un’ von dem dauernden Rufen nach dir ganz erschöpft war un’ einschlief, da war mir fast das Herz gebrochen, weil du verloren warst, un’ mir war’s ganz egal, was aus mir un’ dem Floß wurde. Un’ als ich aufgewacht bin un’ dich hier gefunden hab, heil un’ ganz, da sind mir die Tränen gekommen, un’ ich hätt auf die Knie niedergehen un’ dir die Füße küssen mögen, so froh bin ich gewesen. Un’ du hast an weiter nichts gedacht als bloß daran, wie du ‘n alten Jim mit ‚ner Lüge zum Narren halten kannst. Das Zeug da is’ Plunder, un’ Plunder sind Leute, die Dreck auf den Kopf von Freunden streun un’ sie beschämen.«
Dann stand er langsam auf, ging zum Wigwam und verschwand drin, ohne noch irgendwas zu sagen. Aber das genügte. Ich kam mir so gemein vor, daß ich am liebsten ihm die Füße geküßt hätte, damit er’s zurücknahm.

— Both quoted from: Emer O ́Sullivan: "Zuhause im fremden Text. Sprachliche Identität in Übersetzungen", 1000 und 1 Buch, (1), 4-13. 2013. (PDF) Attempted translation of GDR version back into English:

"What they mean? I'll tell you what they mean. When I was exhausted from work an(d) the constant crying for you an(d) fell asleep, my heart was almost broken because you were lost an(d) I didn't care what happened to me an(d) the raft. An(d) when I woke up and found you here, all healed, my tears came, an(d) I would have gotten down on my knees an(d) kissed your feet, so happy I've been. An(d) all you could think of was how you could fool ol(d) Jim with a lie. "This stuff is junk, an(d) junk is people who put dirt on their friends' heads and embarrass them."
Then he got up slowly, went to the wigwam and disappeared inside without saying anything else. But that was enough. I felt so mean that I wanted to kiss his feet and make him take it back.

— my back-translation attempt

The main point to observe is that most of the peculiarities in language vanish. Basically, Jim's character is marked by using a lot of 'and' (like "en" originally) and then omitting just the final letter 'd' from 'und'.

Whether 'they' justified that as again as idealised 'role-model English' lifted to a more standard one or not may be up to debate. A 'perfect' translation with interlinear word-for-word correspondence would be impossible anyway.

'The book' was printed, and available, the exact version — or even specific editions, if one had set a mind to getting 'that one' — usually not. But that is also translation hell. Jim's exact language was subject to considerable variation in West German translations as well. And also the 'unwanted language' is still a big issue for most modern editions. (Noteworthy: Huck was strictly seen and marketed as 'a children's book'.)
— Dieter Petzold: "Die Rezeption klassischer englischsprachiger Kinderbiicher in Deutschland", in: Hans-Heino Ewers, Gertrud Lehnert & Emer O'Sullivan: "Kinderliteratur im interkulturellen Prozeß. Studien zur allgemeinen und vergleichenden Kinderliteraturwissenschaft", J.B. Metzler: Stuttgart, Weimar, 1994.

Other examples for editions printed in the GDR:

— Mark Twain; Illustrator Hanns Langenberg: "Die Abenteuer des Huckleberry Finn", Greifenverlag: Rudolstadt, 1952.

— Mark Twain & Barbara Cramer-Nauhaus (transl): "Huckleberry Finns Abenteuer - [Vollständige Ausgabe]", Dieterich: Leipzig, 1956.