In the very first several minutes of Godfather I, Vito is disdainful of the mortician's request to have the boys who assaulted his daughter killed -- "That would not be justice; your daughter is still alive." And later Vito says, No matter what this undertaker says, we are not murderers.
However, after Vito's death, at least one man is indeed killed for business reasons -- Moe Greene simply refused to agree to a purchase of his casino as far as we know.
So did the family change with Vito's death or was Vito being disingenuous and in fact, was willing to murder for business reasons all along? In II, the murder of the "Black Hand" guy was in response to a threat of violence -- Vito had seen the man hold a knife to the throat of the young actress so his murder was not just for business reasons.