I heard that they supposedly received limited support from the government, so at least in the party there must have been sympathy. But how was the public perception of the anti-capitalist terrorists across the border like?
From an earlier answer of mine
An accurate picture of public opinion in the Eastern bloc is very hard to obtain, especially for this topic given that much of the information on the RAF would have come from GDR press organs which often presented a very skewed perspective on terrorism. For example, one of the more notorious acts of German Autumn was the murder of Jürgen Ponto on 30 July 1977. The GDR papers only gave a very cursory coverage of the murder of this chairman of the Dresdner Bank. A short 1 August notice on page 7 of Neues Deutschland notes that a chairman of the "FRG monopoly bank" had been shot. Similarly, Berliner Zeitung's initial notice claims that "no motive for the act has be revealed." The next day, Die Neue Zeit's brief report claims the initial aim of the crime was to kidnap Ponto for the purpose of extorting large sums of money. Each of these three papers also note that FRG police have begun wider dragnets of German cities. An 18 November 1977 Neue Zeit report claimed that the murder of Hanns Martin Schleyer have led the FRG to clamp down upon activists such as the left-wing Bund Demokratischer Wissenschaftler.
This lack of contextualization presented a skewed picture in which the security forces of the FRG allegedly used isolated crimes as a pretext to suppress the left. This was very clear in Neues Deutschland's coverage of the Schleyer kidnapping. In a 14 September 1977 article "The Case of Schleyer's Kidnapping," the paper never identifies the kidnappers' group, preferring to call them a "terrorist band," and that the West German Deutsche Kommunistische Partei (DKP), had
alone of the political parties operating in Federal Republic has properly assessed these events. Its estimation of the events, which have been similarly disseminated in the mass media of the GDR, had condemned the terror attacks and has stated that "this and prior terrorist attacks by adventurers, are not part of the working class movement and have nothing to do in the slightest with the imperative struggle for the social and political interests of the working classes."
The article further contends that the kidnapping of Schleyer and the murder of his driver was used as propaganda in the FRG against everything "that can be associated with "the left," and these propagandists are using these isolated acts to sabotage detente and Ostpolitik.
The GDR press's highly selective reporting of the RAF and its activities hewed to a relatively simple pattern of vague descriptions of terror acts followed by highly specific and condemnatory coverage of the FRG's police and state reaction to these events. Coverage of Ulrike Meinhof's death in her prison cell in the GDR often cast doubts on her suicide but also impugned the FRG's justice system that was a tool that suppressed Germany's working classes.
Reporting on the RAF also gingerly avoided explicit discussion of the latter's ideology. The DKP's response to Meinhof's death, dutifully reproduced in 12 May 1977 edition of Neues Deutschland, engaged in a direct attack on the FRG, but also the terrorists. The response condemned the FRG's criminal justice system and engaged in conspiracy-mongering, but also asserted that:
Anarchist adventurism brings no step forwards, but rather a dead end. Maoist or Trotskyite activism is not in the workers' or people's interests, but blunders into the side of reaction. Sham revolutionary actions provide the most reactionary circles a pretext for the denunciation of all the left and progressive forces, as well as their attacks on democracy and freedom. For the younger generation, it offers no future.
The attitude of the GDR press was emblematic of how the SED state perceived groups like the RAF. The state leadership perceived left-wing terrorism as slightly useful, but was very leery of their ideology. The Stasi did engage in some training of the RAF and allowed the RAF to operate within the eastern bloc and the GDR was something of a safe haven for RAF operatives. The second generation of the RAF in the 1980s was more professional than earlier cohorts and was much more successful at evading capture likely because of this training. Department XXII of the Stasi, ironically officially charged with defense against terrorism, maintained a liaison with RAF members and some training. Most famously, in March 1981, RAF students were given training on a RPG-7 attacking a limousine. In September of that year, RAF Kommando Gudrun Ensslin launched a failed attack using an RPG-7 on US General Frederick Kroesen while he was in his armored Mercedes limo with his wife. Although there were enough fingerprints of the Stasi on this attack to bring charges against the Stasi head Erich Mielke after reunification, the courts could not establish a firm legal connection between the practice and the attack for this particular charge.
Despite these attacks, the Stasi leadership in general looked askance at the RAF and its associates and saw their relationship in pragmatic terms. The GDR provided RAF members asylum and would often extensively debrief these asylum-seekers for descriptions of FRG intelligence agents, police practices, and other items of use for the wider intelligence war. RAF attacks also acted as a useful way to gauge the FRG's response network and gain an inkling of how their counterparts reacted to a crisis. RAF members were also an asset for operations within the Third World and the Stasi employed several RAF members in Iraq and Lebanon in the 1970s and early 80s. Despite this support, many within the Stasi saw the RAF as a potentially dangerous rogue element that threatened conventional operations. Conversely,many within the second generation RAF found their GDR hosts to be patronizing and never gave them proper follow-up support or advanced weapons to conduct their attacks. The relationship of the Stasi to the RAF mirrored the larger relationship of this terrorist group to the GDR: both sides tried to use one another for their own ends, but neither got what they fully wanted.
Sources
Aust, Stefan, and Anthea Bell. Baader-Meinhof: The Inside Story of the R.A.F. Oxford: Oxford University Press, 2009.
Gieseke, Jens. The History of the Stasi: East Germany's Secret Police, 1945-1990 New York: Berghahn Books, 2014.
Koehler, John O. Stasi: The Untold Story of the East German Secret Police. Boulder, Colo: Westview Press, 1999.
Schmeidel, John C. Stasi: Shield and Sword of the Party. London: Routledge, 2008.