How would this effect domestic views on the movement and the war itself?
Probably a break-even.
I think if you're someone who already hates the AWM, you're hatred is gonna continue on at about the same degree as before, neither enhanced nor diminished.
At worst, it'll merely confirm your suspicion that they're all a bunch of violent thugs, but on the other hand, RFK is probably someone you never liked to begin with, so you're just gonna think "Ah, the psycho anti-American Left eating its own, so who cares".
And if you're someone who likes the AWM, you're probably gonna know that only a very small section of them are the kinds of people who would kill Robert Kennedy, by that point a major anti-war candidate. So, you'll think "Well, nobody I know in the movement would do something like that, so this must be a pretty fringe element". You might even think it's a false-flag, designed to discredit the AWM by taking out someone who, conveniently, the Right never liked to begin with.
The only way it might have larger repercussions is if the assassin is found to have been part of a wider criminal conspiracy, with a membership list overlapping with more mainstream-allied groups, like maybe Students For A Democratic Society(or whatever they were calling themselves by that point). Tom Hayden might find his political career put on indefinite hold, for example.