He might be a politician, but Billy Bulger sure isn't living life on the straight and narrow.
As a state senator—and a president of the senate, no less—Billy Bulger is known as a conservative firebrand: "a petty despot and a masterful conciliator, [...] a puckish public performer who had a dark side and took all slights personally" (1.2.21).
Sure sounds like a guy you'd want to invite over for dinner.
We can see this conservative streak in his freakout over federally-led efforts to integrate Boston's public schools. Billy claims that he doesn't oppose the efforts on racial grounds, but because it represents the government taking control of his community. As a lifelong Southie, there's nothing that Billy hates more than an outsider trying to boss South Boston around.
Despite his pristine public persona, however, Billy is a total Bulger, which is to say that he does some shady stuff. At one point, we learn that he's involved in a corrupt real estate worth well over a million dollars. Though the politician is able to easily weasel himself out of trouble—thanks to the FBI—it confirms all our worst suspicions of Billy.
He's not Whitey if Whitey was a respectable guy—he's Whitey if Whitey wore more expensive suits.
Although he's never sent to prison or formally punished, Billy watches his public career go up in smoke after the extent of Whitey's misdeeds is revealed. Seems like a fair punishment for a man who ran roughshod over the state senate only through the help of his brother…who ran roughshod over South Boston's streets.