They may not be the only driver of that discourse, or even the primary origin, but they're arguably the face of that viewpoint.
Because of that, the green parties in most countries sold their votes in exchange of policies against nuclear as a first priority.
Are there green groups that support whaling? Coal-fired electrical plants? Global climate change?
There are any number of other problems that "green parties" have in common. Having said that, it's important to note that Greenpeace and Sierra Club are not green parties, but non-profit organizations.
The line is much blurrier than you might think. The green parties originate directly from those movements and there's significant exchange with the non-profit world.
And yes, whaling or coal plants aren't pushed as much as nuclear as a subject, that's not even close.
I think it's because Green Peace's stunts against whaling got them lots of press and made them the most famous of the green organizations.