The non-Jewish victims
One of the main features of the plot is the wrongful racism against people who don't even belong to the race they're being accused of belonging to. For instance, Newman, in a seemingly divine arrangement, ends up suffering the persecution he used against others. He is forced to learn the true consequences of hatred, but this time, he gets to be the falsely accused scapegoat against his will.
The irony of race guessing
One of the questions the novelist asks so well is this: why do people assume they can guess another person's heritage with any real accuracy? Because of racism in America, Irish people and Jewish people were severely oppressed in cities like New York and Philadelphia, but since those ethnicities are sometimes ambiguous (because after all, they all look a little like "normal" white people). This means that in order for racism of this kind to be so prevalent, people had to make blatant assumptions about each other's race, which you can't defend against, because after all, who would admit to being Jewish when an Antisemitic person is threatening them? It's stupid, just like regular racism.
The irony of violence
Another problem in these communities is violence. Now violence is already bad enough in urban areas because of gang culture and the criminal element, but nothing is more threatening to the characters in the book than their own skin. It's not cops or robbers who are harming people—it's the other civilians, possessed by anger and hatred, and usually, they're not even attacking someone of the ethnicity they're hoping to attack.
The irony of tribalism
The novel raises the question of tribal identity. Because most people don't really understand how differently from them people can be, there is a tendency toward fear and xenophobia, rejecting foreign people the way we reject foreign tastes or smells—with disgust. This, combined with our tendency to tribalize, means that in diverse communities, people could start to feel as though they were at war with people from different communities. Paradoxically, this means that everyone really is in a war state with different communities, and suddenly no one is safe. Before the suspicion and paranoia, things were relatively safe.
The irony of the final epiphany
When Newman learns his lesson, he does something that the reader wasn't expecting. What about being treated "like a Jew" made Newman aware that he couldn't trust his wife Gertrude? Perhaps it was the intensity of his suffering, and the way he knew Gertrude to be about suffering. Or maybe, it was that the harsh wake-up call of his mistreatment made Newman more suspicious of other people, having had his sense of safety removed by his first real victimhood.