Organized crime groups with origins in Ukraine often are Jewish, Moscow gangs are mostly not. There were also Moscow gangsters, who didn't have a drop of Jewish blood in them, that acquired Israeli passports. Sergei Mikhailov is the most famous example of course.

I don't live in New York so what I know might mean nothing, but from what I've read the vast majority of "Russian" gangsters in Brooklyn came from or were at least connected to Odessa. Odessa was probably the main centre for organized criminal activity in Ukraine back then. And the majority of the Odessa gangsters (and the Odessa-connected ones) were indeed Jewish. The Odessa group is also a different animal than the Moscow-based groups such as the Solntsevskaya or Izmaylovskaya gangs that later spread to the USA and that consist -with some exceptions of course- for the most part of ethnic Russians. They might have connections to each other of course.

Here in Belgium, in Antwerp there were also members of the Ukrainian group active for some time: Rachmiel Brandwain, Moshe Ben-Ari, the Nayfeld brothers (who were actually from Gomel in Belarus but belonged to the "Ukrainian" gangs),...are some examples. All of them were indeed Jewish and were heavily criticized and shunned by local rabbis and most of the Orthodox Jewish community.
Granted there were also other "Russian" gangs active in the city. The Georgians were also a main factor in Antwerp organized crime. Some of them were Jewish (the Melikhovs for instance), but the vast majority were not. The Solntsevskaya guys had a presence and there were also some Chechen and Armenian gangs. All of these gangs mostly cooperated. An example being a Georgian jeweler (sometimes a Jew, mostly not) selling some jewels to a costumer before a Chechen gang robbed the costumer and brought the same jewels back to another connected Georgian jewelrer.
All of those gangs that came from the former Soviet Union are described as "Russian mafia", while only the Moscow gangs are for the most part ethnically Russian. And those groups, like the Solntsevskaya for instance, aren't even a "mafia" in the strict sense of the word.