'Tis true that Castellano lost a lot of respect in his own family by keeping his distance from the guys in the street and holing himself up in his "White House"; by dissing Neil Dellacroce by failing to attend his wake and funeral; and by openly cavorting with his housekeeper, Gloria Olarte, under the same roof where his wife and daughter dwelled--a big violation of so-called "Mob etiquette."
But the major reason that Gotti found support among most of the Gambino capos was the tried-and-true Mafia common denominator: greed. Castellano squeezed his people unmercifully. Gotti promised them a bigger cut of the proceeds.
Interestingly, Gotti also violated Mob protocol: he failed to consult the Commission before whacking Castellano. But the other Dons were not unhappy to be rid of Big Paul. He had been caught on electronic surveillance denigrating them. And they feared that, after his RICO indictment, he might choose to rat them out rather than spend the rest of his life in prison away from his beloved Gloria. But their relief at Castellano's death didn't translate into approval for Gotti. The Dapper Don had "consulted" the other families, but not their Dons directly--only a select few capos whom he knew would support him. One was Anthony "Gaspipe" Casso of the Luccheses, who said he "didn't give a f***" about Castellano. Luckily, Gaspipe kept this opinion to himself, because a few weeks later, his boss and Vincent "The Chin" Gigante ordered him to blow up Gotti and Frankie DiCicco for having whacked Big Paul without their permission.