What is the effect of such a repudiation? Does the person still end up with the seat but outside of the party?

The Illinois GOP ran an ad campaign against him ("say no to the Nazi") and he lost the general election by a 50 point spread. He ran in GOP primary in the next cycle and came in 3rd with just 1500 votes or so, 10% of the Republican turnout.

His nomination in 2018 was a fluke: he ran unopposed (it was a Democratic wave year election --- the Trump midterms, where we flipped the House†, and no Republican wanted to stake any of their time or reputation on a suicide mission to try to flip a safe blue seat). The IL GOP is unlikely to make the same mistake again: if Jones (the Nazi) appears on the ballot again, he'll have opposition, and it will depants him.

† we flipped the House entirely with moderate Democrats, for what it's worth; the Bernie Sanders wing of the party didn't fare a whole lot better than Arthur Jones did in the IL-3

That's just about the best outcome then. But the way the vermin has been coming out of the woodwork as of late has me worried, too many things appear to be balancing 'just so'.

Yeah, lots of people feel the same way, and there was a lot of chatter among Democrats about Arthur Jones ratifying the racism of the GOP. I get why people might think that, but they think it because they don't pay attention to congressional elections.

It's an underappreciated quirk of our politics that you can't just try to run in a district, just to see how it goes, and then try again somewhere else. You run and fail, and you're often damaged goods for any other race. A bunch of things in our legislative races make more sense when you grok that.