Within historical context, what Sky said was pretty offensive. So is calling another fat but it's not the same thing. I don't recall people being put into compounds and starved or gassed to death for being fat. The slur of being called fat isn't attached to much other than the perception that fat people are not attractive. In a society where there has been famine, a fat person might be looked upon as immorally indulgent. This is pretty different from the Jewish experience at the hands of antisemitic Europeans or Muslims. A WASP gratuitously calling another person a Jewish Bastard is deliberately using the term in the context of the red handed persecutor.
Sky knew she was trolling when she used the phrase. Maybe the cub who was keeping her satisfied recently rejected her and she needed some release. IDK The gratuitous insult out of the blue drew some appropriate fire. That said, Sky got what she needed.
I don't know if Shy is racist or is antisemitic but she uses the language of people who are. Externally observable actions are all anybody has to decide what a person is like. So, Sky is a racist, bigoted asshole. What other conclusion can we draw?