TL;DR: Strom Thurmond and co. wanted to go after Stokely Carmichael and H. Rap Brown.
It took more than half a century for federal courts to seriously evaluate the First Amendment issues in the anti-rioting act… and only after the act was applied to white supremacists (and not the Black activists that Strom Thurmond wanted to target).
Biden gets heat for his eulogy for Strom Thurmond, but in 1985 also he gave a speech praising segregationist Democrat Sen. John Stennis by comparing positively him to Confederate Gen. Stonewall Jackson. From a story I did last year:
The "big switch" is a big lie since, with the solitary exception of Strom Thurmond, NONE of the racist Dixiecrats became Republicans
THE SWITCH THAT WASN'T: Besides Strom Thurmond, can the Left name any Dixiecrats who switched to the GOP? No, because there weren't any!