It is the big socialist governments in history that kill so many Jews.
Yes, specifically National Socialist (Nazi) Germany and the Soviet Union. Both were virulently antisemitic with different techniques. Nazi Germany was committed to Jewish genocide, and exported their genocidal ways to the Jews in the other nations they conquered military. The Soviet Union had a policy of religious and cultural deprivation toward Jews (and to a lesser extent, other religions and ethnic minorities) with periods - notably under Stalin - of "purges" (in reality, exterminations or exiles) of Jews in public positions who incurred the regime's wrath.
Nazi Germany was generally seen as a "right wing" regime during the era of its power, but in retrospect had many similarities to other more overtly "socialist" governments.