There were also prevalent crime issues and ethnic gangs at the time. And many people (Irish in particular) DID go around saying those things you assert no one ever said.
For people who ‘looked Irish’ it was absolutely in their interest to align with these groups to some extent, or they’d be discriminated against and not have useful power to fight against it, and not have a group of people aligned with them that would provide housing, jobs, etc. to them.
In fact, near as I can tell, the only reason the Irish stopped being discriminated against so heavily is because of the political machines and gangs that punished groups for discriminating against them this way.
Same with the Catholics, actually.
So what are you actually talking about?
I don't think, for example, the "mafia" was a major contributor to equal rights for Italian immigrants. One obvious piece of evidence is that today, the mafia has been weakened thanks to the efforts of the police, but Italians haven't become persecuted as a result.
Membership in the Italian Mafia has turned out to be bad on net for the good of the people the families claim to represent. I think some people can get rich doing it but it is not a beneficial or admirable lifestyle.
If you want another example, where were all the Jewish gangs? I'm not aware of a single one. Some famous gangsters were Jewish (at least if you count the movies, I don't know about real life), and I don't think the cause of equal rights has suffered as a result. You have to read this with a smile even though the topic is very serious because the ideas involved would be at home on Saturday Night Live.
One final example is what could be the most hated organizations in America: the white nationalist gangs that only exist in prison. They are all in jail, and equal rights for people of European descent hasn't suffered at all. I'm surprised I ever participated in a conversation where I had a reason to write this, but white nationalists have no positive goals, not even for anybody.
The advancement of the universal recognition of equal rights for all is a much better explanation because unlike the rise of gangs, it hasn't been reversed.
Also your example of white nazi gangs in prison: they exist for the same reason- people need to band together to survive
Which is what you seemed to be rejecting?