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To be clear, Red Orchestra was an umbrella term used by the Gestapo for anti-Nazi resistance movements in Berlin, and for Soviet espionage rings operating in German-occupied Europe and Switzerland during the Second World War.
The main units that came under the term Red Orchestra were:
The Wikipedia page Red Orchestra (espionage) gives the names of the leadership of these groups:
The Trepper unit was led by Leopold Trepper. Trepper was Jewish, and an agent of the Soviet GRU.
'Red Three' was led by Alexander Radó. Radó was also Jewish and an agent of Soviet Intelligence.
The Schulze-Boysen/Harnack group was led by Harro Schulze-Boysen, his wife Libertas Schulze-Boysen, Arvid Harnack and his wife, Mildred Harnack. None of them was Jewish. All were anti-Nazi activists. Harro Schulze-Boysen was an officer serving with the Luftwaffe. Mildred Harnack was an American citizen.