I had a vague understanding that he had a bad reputation, but always assumed it came from more of an "anti-nuclear activist" angle (because he was responsible for making nuclear weapons real).
The fact that we didn't is good luck, but it could have gone different during many points in the cold war and then you and I wouldn't be able to discuss about this on here. But if you knew about Oppenheimer and still were alive you would probably not think highly of the man.
So it doesn't have to do with anti-nuclear (as in: against civil nuclear use) — Oppenheimer was just the prototypical smart guy that failed to predict the consequences of his own actions and by that nearly ended humanity. This makes him an ethically ambivalent figure, and that ambivalence has become a defining trait of the public image of Oppenheimer.
That's not my understanding. I don't think you have anti-nuclear activists that are totes fine nuclear weapons and just don't like powerplants. The activists who oppose civil nuclear use are a strict subset of a broader anti-nuclear activist set that includes nuclear disarmament.
https://en.wikipedia.org/wiki/Anti-nuclear_movement:
> The anti-nuclear movement is a social movement that opposes various nuclear technologies....Major anti-nuclear groups include Campaign for Nuclear Disarmament, Friends of the Earth, Greenpeace, International Physicians for the Prevention of Nuclear War, Peace Action, Seneca Women's Encampment for a Future of Peace and Justice and the Nuclear Information and Resource Service. The initial objective of the movement was nuclear disarmament, though since the late 1960s opposition has included the use of nuclear power. Many anti-nuclear groups oppose both nuclear power and nuclear weapons.
Which is also a bit funny seeing as Oppenheimer was opposed to the H-bomb and the whole nuclear arms race.