We're from the same country, so I know a bit about it.
There was always a fear of contamination, and the Three-Mile-Island accident in the US didn't help. This was before Chernobyl. But of course it's worth remembering why everyone thought that might be such a big problem: there was a siren each Wednesday reminding people that we're in a Cold War, and if it turns hot there's a nuke somewhere with "Copenhagen" written in Cyrillic. So people understood that nuclear fallout is not nice. Plus Denmark ain't big, so basically if something were to happen the whole country could be radioactive. For the same reason, many Danes took issue with the Swedes building a nuclear plant that you can still see from Copenhagen.
The OOA (the organization that led the anti-nuclear movement) made a nice logo with a smiling sun and a "Nuclear Power? No Thanks" message that got thousands of people on the street to protest. Some of the people maintained that if we only could solve what to do about the waste, they'd be fine with it. Often the debate has been "if the tech were better I'd be for it".
I'm not sure this is a reasonable decision. Tech gets better with experience, and you don't build experience by not engaging. Much like mini-mills from Clayton Christensen, often the tech that wins looks crappy and niche when it starts.