Did he ever publicly discuss this cooperation with organizations and individuals to whom he and his family are potential targets?
Stephen Miller has not (yet) admitted to even having produced those emails, so asking for his rationalization of antisemitism is a bit premature.
However, one need only look at his background to see what kind of person he is. Miller grew up in Santa Monica, one of the most highly-educated and liberal cities in America, and the son of two dyed-in-the-wool rich Jewish liberal Democrats. His political activism started in middle school when he read 'Guns, Crime and Freedom' by NRA CEO Wayne LaPierre as a rebellion against his parents, city, and state, all of whom are anti-gun.
He is a prototype of the alt-Right movement: rich, smart, educated, and yet totally isolated from even a hint of adversity growing up but wanting something to rebel against. Classmates in high school say he enjoyed riling up his liberal and nonwhite classmates with controversial statements and compelled Latinx classmates to 'speak only English'. He wrote a letter to the editor at age 16 condemning his high school's (inclusivist) response to September 11th, stating that "Osama bin Laden would feel very welcome at Santa Monica High School". This is a guy that never evolved beyond the adrenaline rush of trolling people in middle school and has turned it into an extremely successful career.