The Nazi characters, at least, aren't really put in a position where racist name calling would make sense. They're mostly talking to other Germans or white Americans. The one part that sticks out is Joe's friendliness to the black ship crew andThe again, I think breaking from the Nazis for ideological reasons is where his arc ultimately goes.regret that they got killed by the Nazis.
As for Chilldan, I remember him voicing very negative things about the Japanese in Season 1. I can't remember too well, though.[/spoiler]
I don't really have complaints against the depiction of the 'bad guy' Nazis. They do use racist invective re the Japanese (they used 'slant-eyed' I think in the pilot ep even). And as you say, there's not much need for racism when you've practically exterminated or driven from the public eye non-whites. The most touchy way Nazi ideology would affect most average Aryans' everyday lives would indeed be their attitudes and policies towards 'useless eaters' and measuring women by their ability to pump out and raise babies, as depicted in the show. I think that part is quite accurate. Ironically, it's in the multiracial Japanese Empire where racism would be a more day-to-day issue.
I think you might be right about where Joe's arc is heading, and that would be interesting but further feeds into the saintly protagonists trope where a racist thought never seems to enter their pretty little heads.
You're also right that Childan is privately disparaging towards the Japanese in season one, but explicit admiration of the Germans/Nazis is never really touched upon.