Modified from an earlier answer on "was the GDR a racist nation or not?"

This is a tricky question to answer as it has two questions enfolded in it "was the GDR state racist?" and "was GDR society racist?" and answering both necessitate a degree of broad generalizations. There is a further complication in that the GDR was never had huge immigrant population. The state tightly controlled the number of immigrants into the GDR and the majority came in as part of work-deals with other sovereign states affiliated with the Eastern bloc. Thus the non-European population was always a very small part of the GDR as a whole and was socially and economically quarantined. To give an example of the peculiar nature of foreigners in the GDR, when popular unrest reached a boiling point in 1988/89, many Communist nations such as Cuba and Vietnam unilaterally withdrew their nationals lest they catch this German political contagion.

Tackling the issue of state racism and nationalism, the GDR portrayed itself as the antithesis of the Third Reich and the capitalist world exemplified by the FRG. Racism became a symptom of capitalism standard Marxist-Leninist orthodoxy and therefore the GDR state operated on the assumption since there is no capitalism within the GDR, there can be no systemic racism within its society. Therefore the state saw no need to combat racism among its employees in state-owned industries and complaints about treatment fell on deaf ears. The strained economy of the late 1970s and 80s exacerbated the state's tendency to exploit these foreign workers. This relationship led to odd situations where fully trained doctors from Africa found themselves doing grunge work like cleaning bedpans. The anti-racism of the state became a convenient pretext for the GDR authorities not to be proactive in the special needs of its foreign workers since all citizens were equal and nationality an artificial construct of bourgeois capitalism. Similarly, as it became clearer that the GDR had failed to deliver the prosperity that the FRG had already achieved, the Honecker regime sought to accentuate localism and the GDR's quaint sense of Heimat as a means to recapture the moral high ground as to which of the two Germanies was representative of the true German soul. These Heimat festivals were highly politicized and the SED actively encouraged volunteerism. As opposed to the cold Zivilisation of the West, the SED stressed that socialism in had tapped into the true German Kultur and made it available to the people. In the 1970s and 80s, local Heimat celebrations mushroomed and emphasized the German particularism of the eastern half of Germany.

The state's willful ignorance of xenophobia dovetailed with incidents of racism within the GDR's society. News outlets would not report on antiforeign sentiments. The influx of guestworkers also meant that racial slurs like "camel-driver" entered into the slang lexicon of the GDR. In a reverse of the experience of the FRG where guest workers helped fuel the West's economic expansion, the foreign workers of the GDR introduced another competitor within the GDR's economy for scarce resources, especially within the black market as many of these guest workers needed to supplement their meager incomes. Non-German students within the GDR frequently experienced such racial taunts in their classrooms and teachers were reluctant to discipline their students. Worker evaluations often had harsher language for non-Germans and the state turned a blind eye to these complaints. The Aussteiger (social dropouts among the GDR's underemployed youth) also added further element of racism within society as many of these disaffected drifted towards skinheadism. This is not to say that every GDR citizen was a racist, but rather there was a strong element of racism within the body politic that the state did not reign in and the state-run economy's shortfalls exacerbated.

The Heimat drive also backfired somewhat on the SED. While it did produce a strong grassroots localism, many of these new Heimat activists became to see (or already saw) the SED as a foreign intrusion onto the local. The GDR's woeful environmental legacy drove a further wedge between local activists and the state, especially after increasing use of brown coal and the Chernobyl disaster underscored the Eastern bloc's failure in this regard. Heimat activists would demand that the SED be held accountable for the degradation of the German landscape. Unlike the churches or other "bourgeois" elements, the SED did not predict that environmental activism would emerge as a source of criticism.

Now as to how much the former GDR created political sentiments like PEGIDA, that is a difficult matter. The rough economic transition to a free market, the condescending attitude of some Westerners to the East, and the disappointments of reunification contributed to a kind of contrarian politics in the east. Reunification also brought East Germans into increasing contract with foreigners without the state acting as an intermediary and regulating their contact. This situation exacerbated the preexisting sentiments the SED encouraged, like localist nationalism, or ignored, like racism.

How much this could have been avoided with a better political and economic transition is a sticky wicket; while there is something of a reciprocal relationship between a rough reunification and preexisting mentalities, there are other features at play. In the case of anti-Islamic movements, it is important to contextualize movements like PEDIGA with the rise of similiar anti-immigrant and nativist movements throughout Europe. German developments did not happen in a vacuum, but exploring them would necessitate breaking the twenty-year rule and incurring the wrath of the all mighty moderators.

One concluding caveat is in order here though. While the GDR's position that there was no racism in the worker's state was hypocritical and self-serving, the general narrative of non-Europeans within the GDR is roughly similiar to their Western counterparts. These guest workers and migrants often had ghettoized housing and segregation, suffered racial slurs and taunts, and the FRG state was just as capable of turning a blind eye to this problem as its Marxist-Leninist analogue. The issue of integrating non-Europeans into the social sphere was a thorny one and the shortcomings of the state and society to live up their promises was a problem on both sides of the Iron Curtain.

Sources

Ireland, Patrick R. "Socialism, unification policy and the rise of racism in Eastern Germany." International Migration Review (1997): 541-568.

Palmowski, Jan. Inventing a Socialist Nation: Heimat and the Politics of Everyday Life in the GDR, 1945-90. Cambridge: Cambridge University Press, 2009.

Pence, Katherine, and Paul Betts, eds. Socialist modern: East German everyday culture and politics. Ann Arbor: University of Michigan Press, 2008.