The key to answering this question may be in the dialogue of another movie: American Gangster. Richie tells Frank Lucas that, to the Mafia, a smart business man like Frank represents progress. In his absence, everything can return to normal.

The Corleones made their money off of normalcy. That's one reason why Vito turned down Sollozzo; he did not want to disrupt that which was normal. Over the past several decades, Republicans have come to represent normalcy more than Democrats. It may have been different in the 30s and 40s.