Hashi/ Tobirama ------ Kagami >>> Shisui >>> Itachi...
if they didn't influence Itachi.. well Itachi already admitted to doing things wrong and becoming dependent on his own power and being almost arrogant.. or maybe just over confidant and trying to do everything on his own.
but since he was 4years old he knew how horrific War was and he had a Hokage level brain when he was 7..
so I don't think the hatred would have affected his mind & heart..