You do understand the other side's situation right? You are, albeit impersonally, being accused of participating in something monstrous, the institutional subjugation and prejudicial treatment of an entire class of people, and there is literally nothing you can say or do which will demonstrate otherwise since your racist acts are unconscious and unknowable to you.
It's like trying to convince someone that you're not crazy when they already think you are. It doesn't mater, anything you say or do just reinforces their belief.
We all hold biases and prejudices for just about everything from concepts, ideas, products, institutions, and especially one another based on their history, race, creed, social status, clothing, voice, stature, hometown, manner of speaking, educational background, career field, job title, wealth, attractiveness, political beliefs, the list goes could go on for pages. But trying to equate these kinds of biases to being *-ist in any meaningful sense is missing the forest for the trees.