1. Organized crime is made of people who view society fundamentally flawed. Everyone is a puppet on the end of someone's string, and that someone gets to hold the moral high ground whether or not they earned it. These people who band together can form their own version of society, on which they can impose their own sense of justice, crooked though it might be from our perspective.
2. Those groups can be found just as easily in regular society. Wiseguys don't do work for anyone but themselves, and they take advantage of whatever code they can. They only look out for themselves, and anyone who they have something to gain from supporting. Suckers take the status quo at its word; they believe in America as a just meritocracy where everyone is on equal footing, and hard work will win the day.
3. At the beginning of the Godfather, Michael is probably a sucker in some ways. He went to college for a moment, and served in the war. Later, (or earlier) Sonny talks about war as fighting for someone outside the family. The rest of the Corleones are either sharpies or wiseguys, depending on their proximity to the power in the family. Michael obviously transitions out of the sucker phase he goes through, as he likely would have eventually through legitimate means; his father intended for him to become Governor/Senator Corleone.
4. Nick is obviously a sucker; he refuses to accept a place in Gatsby's network, and is off-put by Wolfsheim. Wolfsheim himself is a wiseguy, as he is pretty content to take advantage of people around him.
5. The American Dream, for it to be American, has to be a possibility for everyone. There are plenty of people who have no way to access that dream, and in attempting to find a path to it, find themselves on the crooked ladder. Though the Alger view of the dream is closed-off to these folks as soon as they make that transition, another path presents itself. If the American dream is defined as generally as possible, it's difficult to disrupt that dream without getting rid of the entire system. Any more specific meaning applied to it finds roadblocks at everyone corner for anyone who isn't the ideal. Those roadblocks can be circumvented, though, by a new worldview in which said roadblocks are no longer obstacles, but side effects. You might have problems with the police, but there's food on the table and excitement to be found anywhere.

Gangsters discussed here may still participate in organized crime, but the respectability they have obtained doesn't depend on their living. If they maintain the charade of legal affluence described in the Bell quote, there's no discernible difference between the criminal and the college professor.

It's not impossible to believe that society is corrupt and to still want to work within it. Some people believe that they can change it, or that they're skilled or tough enough to get by despite that corruption. Plenty of people really did recognize the larceny that Luciano mentions in the quote from page 148, and they really are just too scared to do anything about it.

This idea is easily seen when it comes to genres that have less basis in reality. Fantasy and science fiction are filled with practically mandatory tropes that are fulfilled in ways that don't connect to reality at all.

While Jay Gatsby is portrayed as a gangster, it doesn't immediately follow that The Great Gatsby is a gangster novel. The brutality mentioned as inherent to the genre is largely absent from the bulk of the story. Gatsby dies a violent death, but not with a gun in his hand.

To a certain extent, everyone's external image is different from the personal idea of themselves. In the context of the quote, a celebrity's external and internal personas can be so radically different as to become unrecognizable.