Is it a New Jersey thing?
I don't remember the exact year, but Bialys got some not insignificant attention in the media around the time the the Sopranos was being produced. This may have been an influence, or it may simply have been the show putting light on a beloved, but not-well-known comestible.
My understanding is it is more of a Lower East Side/Brooklyn thing, but the mob goes way back in these neighborhoods.
Mel Brooks was undoubtedly referring to the food in choosing this name.
(Also "Biały is Polish for "white". The word is a Polish surname, as well as a nickname of several Polish monarchs and noblemen.")
This may be related to the way Paulie described "Elvis Country" -- a place where there are no Jews or Italians. While I think it was Paulie himself who used the term "Christ Killers" against Jews, there has been historically some affinity between the Italian and Jewish communities and not just in the mob. Italians lived and worked with Jews, having come over at the same time in large numbers in the late 19th and early 20th centuries. Note that while Hesh is not a member because that would always to limited to Italians, he is definitely an associate who is on friendly terms with Tony's gang although we saw also that when it comes down to it, there is a strong divide. Anyway, bialys in the United States was primarily a food associated with Jews, Bialystok having been a large city from which literally tens of thousands of Jews immigrated.