At what point do immigrants to Italy become accepted as bein "Italian"

Its been said that after a family is in Rome for seven generations,then they are Roman? Is that true or will they always be see as non Italians,whether it is German,French,Nigerian,Arab,Jewish,Ugandan,etc/

Is it different for white European immigrants to Italy that for black,or Asian immigrants as to whether or not ther descendants would ever be considered Italian in ther sense of actually assimiliated and accepted.Not talking about citizenship.