I think it's generally true that the only ways an accusation is going to hurt a person's feelings is either if it's not true, or if it is true, and something that the person is ashamed of. If you accuse a person of something that's true, and he or she is proud of it, then he or she won't be hurt by the accusation.
So, there is an answer to the question of how you can disprove an accusation that you're a racist. Well, it's simple, the person who makes that accusation directly to you is trying to hurt you, or get you to think twice about what you're saying. So, the person making the accusation knows that you're not a racist. The fact that the person thinks that the accusation is going to be effective means that the accuser already has it in his or her head that you're not racist; or that you are racist, you're aware of it, you're embarrassed by it, and you're trying to work on it.
Think about this.
If you see a dude with a swastika tattooed on his face, and you want to hurt his feeling or get him walking on eggshells, you're not going to accuse him of racism. He's wearing his racism on his fucking face.
If you went to the anti-Israel in rally in Sydney on Octber 8th of last year wherein they were chanting, "Gas the Jews!", you wouldn't say, "Hey, you're anti-semitic." as an insult. They're literally telling the world that they're racists.
Okay, how about the case that I brought up in which calling a person a racist is true, and still an effective insult. That's like the people who bring up my struggles with alcohol when they start losing a debate. I'm aware that it's true that I've had a problem with it for a long time, and I'm trying to get past it. I think it's pretty well agreed upon that it's a dick move to bring up a person's personal struggles in order to shut the person up. So, the racist who is actually hurt by your accusation is somebody who is already woke, and trying to work on him or herself. It could be a person like Maajid Nawaz or Mosab Hassan Yousef who were born into families and communities that taught them from the cradle that Jews were the spawn of pigs and vermin who are still struggling to deprogram themselves.
Now, to be clear, I'm not saying that every accusation is false. Have been, still are, and probably always will be racists in the world. If you're observing that a third party is a racist, you could very well be right.
It's when you make the accusation directly to that person that makes it pretty clear to me that you know that you're falsely accusing that person. You know that you're lying about the accusation, because you're intending to hurt the person or change that person's behavior.