Andrés Calamaro is not singing about gangsters here. His "mafia" is his circle of friends, and the whole song is a toast to them. He opens with "My mafia es para mí / Mi amistad y mi riñón" (my mafia is, for me, my friendship and my kidney). Calling your friends your kidney is a lovely, slightly gross way of saying they are a vital organ you cannot live without.
He says the bond is "duro como el metal" (hard as metal) and that he thinks "más allá del bien, más allá del mal" (beyond good, beyond evil). In the chorus, "Cuando ladra la moral / En modal inquisición" (when morality barks in inquisition mode), his answer is to sing "a la libertad" (to freedom). Ladrar is what a dog does, so the moralizers are pictured as barking dogs.
Then it gets personal. He names real friends: "el gallego Frank" (Frank the Galician; in Argentina gallego is also a nickname for anyone of Spanish descent), "el gordo Raúl" (big Raúl), plus Osvaldo, Jorge and Adrián, "hermanos por elección" (brothers by choice). The last verse nods to "el día del Amigo" (Friend's Day, a big date in Argentina) and promises he will always sit at the table "de los bandidos" (of the bandits). It is a warm, cheeky song, and "brothers by choice" is a phrase worth stealing.