The movement was already strong before Chernobyl, and I don't know exactly why it was so much stronger in Germany than elsewhere (and couldn't find a clear explanation on Wikipedia either).
Then Chernobyl happened. Germany was, and is to this day, directly affected by the radioactive fallout from Chernobyl. (Many of the boar hunted in Germany are considered unsafe to eat due to high radiation levels).
People remember when they were wondering if they should abort their pregnancies because they weren't sure if they'd give birth to a child with three arms, or too afraid to drink the milk, etc. - most of these fears turned out to be unfounded, but that doesn't mean that people weren't affected by them and remember them deeply.
The Green movement had also built its entire identity around it, making it hard to go back on it.
Fukushima sealed the deal because nuclear power was advertised as safe, not "well it explodes sometimes but the actual damage is less than from coal", any thus the safety claims lost all credibility.