The heads of the Soviet political police were not all of Jewish origin, although some such as Iagoda were.
However, they were strongly pro-Jewish in the same way as the United States Government today is strongly pro-Jewish and supports Jewish interests without question. They invariably crushed any group of people that opposed Jewish interests, such as Ukrainian nationalists.
The first leader of the Cheka, Feliks Dzerzhynskii, was of Polish aristocratic background, but he was heavily judaised through his relationships with Jewish revolutionaries, particularly with Jewish women.
The head of the NKVD during the Great Terror, Nikolai Ezhov, had a Jewish wife and had close relationships with Jewish intellectuals, including Isaak Babel. In fact, it was very common for leading non-Jewish Bolsheviks to have Jewish wives, and there can be little doubt that they were influenced in a pro-Jewish direction by them.
The successor to Ezhov, Lavrentii Beriia, was so virulently philosemitic that it was rumoured that he was a crypto-Jew, which was not true, since he was of Georgian origin. His support of Jewish interests was demonstrated by his immediate action after the death of Stalin to release the Kremlin doctors, most of them Jewish, who had been accused of poisoning Soviet leaders, and to purge the NKVD officers who had accused them.
There was even a rumour that he had killed Stalin himself, in order to halt the anti-Jewish agitation that had accompanied the so-called "Doctors' Plot". However there is no real evidence for that belief.
It is a well-known historical fact that anti-Semitism was a crime under Soviet law, and carried the death penalty in some cases. Prosecution for anti-Semitism was often used as a means of getting rid of political opponents. The most prominent person executed for alleged anti-Semitism was the head of the Crimean Tatar ASSR, Ibragimov, who in the 1920s had offended philosemitic elements in the Soviet hierarchy by his strenuous opposition to proposals for the settlement of Jews in agricultural colonies in Crimea.
There was a joke that circulated in Soviet Russia and, after the Second World War, in the Soviet satellites such as Poland, which is revelatory of the perception among the common people of the relationship between Jewish and non-Jewish Bolsheviks.
It went like this:
Question: "Why are there non-Jewish Bolsheviks (or non-Jewish Chekists)?"
Answer: "Someone has to carry out the executions on Saturdays".
The joke was an allusion to the common East European institution of the "shabbes goy", that is, a non-Jew hired by wealthier Jews to perform all the necessary functions that a pious Jew is prohibited from performing on the Sabbath, eg lighting fires, cooking food, running errands etc.
The "shabbes goyim" were invariably drawn from the lowest strata of Gentile society, and were despised by the general population for being "servants of the Jews".
Hence the purpose of the joke was to imply that non-Jewish Bolsheviks were performing the traditional role of "shabbes goyim", and were as such despicable people, from the dregs of Gentile society.