If Galante did have trouble it would not because he saw them as rivals, that sounds like leak put out by feds. So many stories pop up about him, such as him blowing up the doors of Costello's Mausoleum, another story with no proof.
He obviously pissed off a lot of Mafia people, and The Gambino Family under Castellano did seem to back his killing. The only way Castellano did not know if is if Dellacroce went rouge or was given permission to back it or not back it. The last part i base on the killers of Galente going to The Ravenite and meeting members there.