Do you have statistics to support this?
Usually, Communism, and Socialism for that matter, is led by the middle class and followed by those wanting some food on the table.
In the event your country's Jewish population flocked to the communist banner, well, it isn't a moment to hang out the flags: it simply means they felt so marginalised they nailed their colours to the mast of Extremism.
The Nazis said something like what you're saying, except, as you'd reasonably expect, Jews were represented throughout all aspects of German society and politics.
Around 60-74% of the leadership in the Hungarian Soviet Republic, 60% is usually given as the minimum, the difference is usually depending on who is considered to be in the pool, only the leading comissars (functionaries equal to ministers), or the deputy-comissars too, or also considering personal changes during that 133 days when the 1919 communist regime existed, how Jews were they (full or from mixed parentage, did they baptize or not etc). According to Randolph L. Braham's
The Politics of Genocide: The Holocaust in Hungary out of the 45 comissars of the Kun regime, 32 were Jews or of Jewish origin, that is 71% if i count it well (in a country where 5,9% of the population were of Jewish faith in 1920). He mentions this data in footnotes, I only have the Hungarian edition of this book so i don't give page numbers, but for further reading to this data he also cites
Joseph Rothschild: East Central Europe Between the Two World Wars. University of Washington
Press, Seattle, 1974 p. 148 and
Nathaniel Katzburg: Hungary and the Jews, 1920-1943. Bar-Ilan University, Ramat Gan, Israel, 1981, p. 32-38. Btw I recommend Braham's monumental book in general, still the most authoritative work on the Holocaust in Hungary.
Anyway i don't use it as an accussation, but it is a fact that a big part of the contemporary Hungarian population also precieved the Hungarian Soviet Republic as a "Jewish rule", and the following right wing counter-revolutionary regime exploited it to the maximum extent, to connect the dots to an imagined "Jewish Bolshevism". Still many in the Jewish community opposed the communist regime (most obviously the rich bourgeoisie and the religious), in fact despite its Jewish leadership, the 1919 communist regime itself was not shy to use sometimes the anti-semitic card, equalling big capital and Jews in some propaganda articles in order to gain popularity.
This thing was not alien from even the classic 19th century socialist/communist/anarchist thinkers.
And you are also right, the initial leadership in communist, socialist (and social liberal) movements came from urban middle classes, and in those segments Jews were also overrepresented. So there is no dispute in that I guess, it doesn't change the fact that their overrepresentation gave excellent material for anti-semitic politics in the following years.
I actually understand it and find it absolutely logical that many ambitious Jews from the lower to middle classes were drawn to it, and obviously not to Christian nationalist movements which mostly wouldn't even want to embrace them anyway.
(I've heard some other psychoanalytic explanations too that would link that people with Jewish religious upbringing having more inclination toward revolutionary ideologies due to the Messianistic elements of their religion, but i'm sceptical about that argument, I don't know that much about Judaism)