Quantity can make quality.If some of the NKVD officers were Jewish, so what?
According to the table linked by Oleg at the site http://www.memo.ru/history/NKVD/kto/stattab4.htm,
in July 1936 (when the NKVD was established, absorbing the former OGPU) of a total of 96 senior NKVD officers, 37 were Jewish by nationality, or 38.54%. At the same date, 30 senior officers were Russian and only 5 were Ukrainian; that is to say, the number of senior officers of Jewish extraction was equal to the number of Russian and Ukrainian officers combined.
When we consider the very small size of the Jewish population of the Soviet Union compared with the size of the Russian and Ukrainian populations, which together constituted over half the total, we see that Jews were vastly over-represented in the top echelons of the NKVD. That in turn gives the impression that in 1936 the NKVD was a disproportionately Jewish organisation.
The significance of that is that a typical Ukrainian, seeing the disproportionate number of Jewish officers and the very small number of officers of his own nationality, might well conclude that this organisation of state security that was oppressing him, and of which he lived in fear, was a Jewish organisation, representing a Jewish tyranny over him. That in turn would lead him to hate and fear the Jewish population in general, and predispose him to collaborate in its destruction by the German invaders only five years later.
The over-representation of Jews in the top echelons of the NKVD in 1936 most probably indicates a similar over-representation in the organs of state security going right back to the beginning of the Bolshevik regime. Regardless of whether that over-representation truly indicates that the Bolshevik regime was a Jewish tyranny over the other peoples of the former Russian Empire, what counts is the impression in the minds of the common people and of outside observers, including observers in Germany such as Hitler, when he was writing "Mein Kampf" in 1924.
According to the table at the above site, the over-representation of Jews in the senior ranks of the NKVD continued until July 1937, when their number began to be swamped by the increasing numbers of Russians recruited as part of the huge increase in the size of the NKVD during the Great Terror, which began in July 1937.
However, by that time, the impression of the NKVD as a Jewish organisation of oppression and terror had become indelible in the minds of the people. I think there can be no doubt of a causal link between the longstanding over-representation of Jews in the Soviet organs of state security and the later mass-slaughter of the Jewish population at German hands, which began in occupied Soviet territory and not in Germany, and which in many ways had the nature of an act of ethnic revenge.