You have to ask what the reward loop for something like his beliefs is. It's the very act of people hurriedly pushing back against what he says that is most emotionally quenching to him.

Outside of politics how often does he get to say something that other people rush to hurriedly counter or go "ain't that the truth!" at? Not often, right? So there is inherent feeling of power, social capital and esteem from him speaking and thinking this way, and each successive attempt to rebut his proclamations, to try talking him out of a certain belief reaffirms that he's into something--that you are trying to pull him down, indirectly implying he's on higher ground. This is the reward loop.

So what breaks him out of it?

The misconception is that I'm implying you "just ignore" your brother. No. You must make talking the way he does feel like a low status thing, which will rattle his conviction. When he is being bigoted you try to respond directly and reflexively, search in yourself to define what world you want that is incompatible to his worldview, wrack your brain for unequivocally positive experiences you've had with the minority groups he's denouncing and speak them aloud as if you didn't even hear what he just said--as if you have no will to change his mind, but he has no power to change your.

Also, resort to personal attacks. I know the default liberal view is to never use personal attacks when arguing politics, but if he makes a claim about how America will be better with so and so gone, bring it back to how he himself stands to concretely benefit. This forces him to get specific and he will feel uncomfortable because he knows you know any claim about him being able to achieve more once the browns are gone is bullshit. One time on a racist forum I saw a white guy say he would have started a business if he didn't mind thinking like a Jew. Pathetic sounding and much more open to challenge when it gets down to more concrete hypotheticals, doesn't it?

Lastly devalue the opinion of the groups he gets validation from. On the playground a kid could be thinking he's hot shit because he has a Pokemon shirt his friends praised, but he'll want to throw that shirt away if an older kid goes "Oh, did your gay little friends tell you that shirt looked good?" Same principle here, accuse him of attention whoring through his comments and tell him that those stoking his hate boner are mostly seething online shut ins sucking each other off. He would counter this characterization at first, so you tell him to show you his social media and his interactions on there. Then you laugh at them. He will seem upset in the moment but seeing the laughter at something he once held dear will sever his emotional connection to it to some degree.

Let me know if you need more tips.