Stalin's (Ex-)Nazi Children
Joseph Stalin, also seeking to extinguish Germany as a geopolitical threat to the Soviet Union by ending it as an independent nation, was not personally opposed to working with Nazis (obviously, as seen by the Molotov-Ribbentrop Pact), let alone ex-Nazis. Stalin overruled many other Soviet diplomats and officials, including almost all of the East German Communists, in pushing for the creation of the National Democratic Party, a vehicle for ex-Nazis to be tightly controlled by Stalinist-aligned Secret Police. The NPD leadership was largely comprised of former members of the National Committee for a Free Germany, Wehrmacht and SS defectors during the Great Patriotic War, some of who truly converted to Communism...some who just saw where the wind was blowing. The most prominent member of this group was Friedrich Paulus, the German Field Marshall who surrendered the Sixth Army during the Battle of Stalingrad (he died of old age during the Three Years War).
Under Stalin's pressure, Prussosaxon (later East German) authorities set up the National Democratic Party, a vehicle for other Wehrmacht and SS veterans in hopes that they could be co-opted by the Communist State. They remained a loyal appendage of the Socialist Unity Party ("SED") for several years, adopting essentially doctrinaire Marxist-Leninist principles, agreeing with the government on everything. However, Heinrich Rau, placed into power by Beria after he pushed the SED to hound its hardliners from government (namely both Ulbricht and Honecker), significantly opened up East Germany, both politically and economically. Berlin Spring was in many ways the brainchild of Beria. However, when Rau died in 1961, there was a widespread fear now that like in Hungary, the Berlin Spring would spiral out of control. Beria's hounding of hardliners left him with almost no allies in East Germany. No ally except one.
The members of the National Democratic Party still revered Joseph Stalin, and there was a rather suspicious reverence that emerged from those who were once the least Communistic after Joseph Stalin's persecution of Soviet Jews. The NKVD still had tight control of the NPD and a result, the most slavishly loyal Soviet puppets in East Germany...were ex-Nazis/ex-Wehrmacht members. These Soviet allies also dominated the officer ranks of the National People's Army (NVA) simply because they were the East Germans with military experience - most of them served quite competently in the Three Years War, with East German troops quickly taking back East Austria from Yugoslav troops.
With the NKVD ferociously spreading rumors of a possible NVA coup (or in some cases, just outright threatening it) unless the SED further "liberalized" and selected a leader from outside of the SED (but within the National Front, the SED-puppet parties), a rudderless SED eventually relented. Eventually, Wilhelm Adam, a Stalingrad veteran, co-founder of the Committee for a Free Germany, and Minister of Saxony (whereupon he had implemented most of Rau's economic reforms), was selected to replace Rau. Ironically, the domestic repercussions were not significant. Although presenting himself as a "post-Communist, anti-Hitlerian nationalist", Adam was in fact a loyal Communist who followed NKVD orders and largely governed exactly the way Beria wanted him to - the exact same Rau had been governing. A veneer of liberalization, surrounding a harsh Stasi/NKVD fist.
However, the diplomatic repercussions were significant. First, Adam immediately was celebrated by Otto Remer, the West German neo-Nazi who famously helped foil the July 20th Plot against Hitler. Remer and his Socialist Reich Party was always covertly funded by the Stasi to embarrass West Germany - now he was seen by West Germany as an actual Soviet agent, causing the West German government (heavily influenced by a clique of radical right-wing but not neo-Nazi Wehrmacht officers who had often actually supported the July 20th Plot, chiefly among them Hans Speidel) to outlaw the Socialist Reich Party and attempt to arrest all of their members. Remer escaped arrest, with his members going underground to resist the West German government through urban guerrilla warfare, such as car bombings and kidnapping. East Germany obviously disavowed Remer, though the Stasi did give him all of the bombs and intel he needed. As a result, 1960's West Germany would be more or less gripped by fears of neo-Nazi bombings as West German security forces (ironically also staffed sometimes by ex-Nazis) battled neo-Nazi terrorists.
In addition, the rise of Adam was widely seen in the Middle East as Beria riding to the rescue of the Syrians, since many observers dubiously assumed everyone who annoyed Israel was an ally of Syria. Those observers included actual Nazis, such as Omar Amin, who was known as Johann von Leers when he served under Goebbels before he converted to Islam and moved to Syria to work for Tlass. Stasi agents operating in Syria further allowed the triumphant Tlass to outmaneuver and sideline al-Bizri, as Tlass himself was declared President soon after by a nearly unanimously vote in the Syrian "parliament." Otto von Skorzeny, now unemployed after the end of the Indonesia War (he had fought against the Communists), deployed his men to the Middle East to fight for the Syrians. Ironically, despite receiving plenty of Soviet and East German arms, Skorzeny, aware of the Sino-Syrian Split, celebrated Syria as the only "bulwark in the Middle East from Asiatic Communism." This created a bitter split with his friend Reinhard Gehlen, who was one of the leading coup planners in West Germany and one of the most influential men in West Germany. As a result, Syria quickly became a haven for unrepentant Nazis, such as Alois Brunner, Omar Amin, Walter Rauff, and Aribert Heim (Tarek Farid Hussein after his conversion to Islam), many of who gave the Syrians crucial advice on their next big play in the region. Needless to say, none of this helped Menachem Begin when details of his secret agreement with Syria was leaked.
Of course, the East German regime and the USSR condemned Syria for harboring Nazi war criminals and Holocaust perpetrators (even while secretly funding the Syrians), claiming to take North China's side in the Sino-Syrian Split. In many ways, the Soviets tried to have it both way - totally denying any cooperation with ex-Nazis and constantly lambasting the West German government for its Nazi sympathies, while implicitly also winking at neo-Nazis and giving them the arms and bombs needed to wreck havoc in the West. The development was rather demoralizing to young West German leftists, who saw 1) two competing German governments go at each other, 2) both militaristic, nationalist governments run by ex-Wehrmacht generals with uncomfortably close ties to the old Nazi regime, 3) both of whom constantly called each other Nazis by pointing out those uncomfortably close ties. Worst of all for West German leftists, they were often the victims of terror bombings by these openly neo-Nazi terrorists from the Socialist Reich Movement, terror-bombings that the ex-Wehrmacht generals of West Germany typically used as an excuse...to further clamp down on not only open neo-Nazis, but also young leftists. Left-wing German students were particularly outraged when the the Parliament, including even the Social Democratic Party, voted to shut down several left-wing student campuses in reaction to a neo-Nazi bombing that killed 13 college students from an on-campus socialist discussion group.