The target of the activist is not the government, it is other citizens. The goal is to increase the disapproval and outrage above the activation energy of government agencies or legislatures. Anti-nuke activism hit as the first wave of the environmental movement was peaking (think anti-pollution efforts against some really, really bad industrial practices and the anti-litter movement) and it also pulled in a large swathe of anti-war activists who were looking for their next mission after the Vietnam war wound down. Combine these with some genuine hubris on the part of the nuclear energy industry and a public that has a hard time assessing actual risk and you get a perfect storm of sorts. It was easy to pass regulations and laws that made nuclear more difficult to deploy and casually ignore the consequence that this had on making petroleum products and coal the only viable alternatives.