That explains why they exist, but not why new groups form today still.
Although, yes, the GOP have been enabling and emboldening them for the last (at least 5 but really many more) years - now they have a whole bunch of people who support them in the WH that are dismantling anti-WS task forces etc.
And most of their membership is not a split from KKK etc. It's new people, often with very different backgrounds age- and education-wise. And one distinguishing thing about them is that they put a lot more emphasis on politics and outreach compared to KKK, and they openly reference fascist and Nazi ideas - which is to say, they don't just talk about white supremacy, but they talk about fascist ideals for governance etc.
Make no mistake, this is a new wave of political right-wing authoritarianism in US, not the same old.
I'm assuming you want a more nuanced answer than "because SV is libertarian white dude central"?
> why did these groups form in first place.
Oh, that's easy - because the US has been a racist country for decades and no-one has had the balls to stamp it out.