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 a huge immigration country. 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.

Tackling the state, 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.

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 forign 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. 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 it that the state did not check and the state-run economy's shortfalls exacerbated.

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.

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

You might want to be a bit more specific. What do you think makes "a racist country"?