Loyalty is everything to the Italian American community depicted in A View from the Bridge. Even if people don't necessarily know or like each other they still put on a front of solidarity, standing together as part of one community.
Community solidarity is all-important in this neck of the woods; it is a way of providing some measure of security in an uncertain world. Without the mutual loyalty that binds people together, that solidarity would start to collapse, with damaging consequences for the community as a whole.
In practical terms, this means that people tend to keep their mouths shut about illegal Italian immigrants in their midst. Ratting out illegal immigrants to the authorities would represent a betrayal of the community's values. Many of the people living in this community are themselves most probably illegal immigrants, and so the last thing anyone wants to do is rock the boat. Legal or illegal immigrants, Italians or Italian Americans, everyone sticks together.
Or that's the theory, at any rate. Eddie Carbone betrays the loyalty that people in this community owe to each other by ratting out Marco and Rodolpho to the immigration authorities. Eddie knows full well what he's doing, but he's so demented with jealousy over Rodolpho's burgeoning relationship with his niece Catherine that he's prepared to go against the community's deepest values.
The absolute hatred and contempt that the community has for those who betray the community is expressed most viscerally in Catherine's outburst when she hears what her uncle did:
What're you scared of? He’s a rat! He belongs in the sewer!
What's more, there are few people in the community who would disagree with Catherine.