Honestly I feel like that's even worse because Wallace knew that what he was doing was wrong but still did it anyways in order to get elected
Off-topic but I recall an article in the past year that detailed Newt Gingrich's first campaign as a Carter Democrat. He wasn't running as a racist relict, but rather a pretty progressive guy with a big focus on the environment. It didn't work. He came back a few years later as a hardcore conservative Republican. It's a sad truth about politics: while they're not all soulless power-seekers, you can bet the soulless power-seekers are going to find their way to the field.
As for Wallace, I would imagine there would be some immediate violence in the wake of an assassination. My feeling is that as bad as it would be, it wouldn't rise to the level of national emergency without specific AH triggers. If it didn't, there would be a new round of suffering and news stories and personal reactions that collectively move the country a few small notches in the direction of both greater support for free speech (as a backlash against killing someone over their words) and greater support for the police state (as a backlash against the resulting violence).
If you can somehow force a situation where Nixon has to specifically and unequivocally denounce racist white (southern) violence, that could change things. The South has not integrated into the Republican camp in 1972, and this could be the end of that relationship. It could also force the Carter mold to form up with a bit more vigor and purpose. You could see a more progressive streak in the median white southerner who is forced to confront worsening racially-motivated violence.