Rodney King as a symbol of injustice
Rodney King was a man who was assaulted just before the LA riots, and the police officers who abused him were famously acquitted of those charges, causing the riots. This is so meaningful to Macon that he gets the date tattooed and shows it to black people whenever he can.
Macon's tattoo as a negative symbol
When Macon shows his college roommate the tattoo he has of the date of the infamous King verdict, he doesn't know that his roommate was literally there, experiencing it for real. So the tattoo represents the irony that Macon isn't actually involved at all in the real struggle against injustice, but he stakes his entire identity on that struggle as if he were black. It's actually just a symbol for cultural appropriation.
The motif of "Blackness"
Throughout the book, we learn annoying little details about Macon's identity. For instance, he hates the Beastie Boys because they are white people using black musical ideas to entertain other white people, and yet he is literally pretending to be black so he can feel like a victim instead of a problem. He appropriates black culture in his identity while hypocritically hating other people for getting it wrong.
The symbol of the gun
This novel breaks one of Chekov's rules by including a gun that doesn't actually get used, but perhaps it's supposed to be a symbol for Macon's ineffectiveness as an activist. First of all, it means he is hateful and violent. It also represents Macon's desire to be a radical. But nevertheless, he just uses it for power, which also is how he handles race relations in general—he will believe whatever makes him feel the most powerful.
The symbolic "Day of Apology"
Mansbach uses a rhetorical device called "Reducto ad absurdum," where he takes an idea all the way to its conclusion in order to show that the idea is flawed. Suppose Macon finally gets traction and gets what he wants. What is it that he would do in that position? He would have all the white people drive into the 'hood' to say sorry to all the black people. The silent criticism is that of course Macon wouldn't have accomplished anything except being really annoying and offensive.