1. Any equipment or substance that is both nuclear and potentially dangerous has some sort of magical mutant super-power to stimulate superhumanly idiotic behavior in a non-trivial fraction of the people handling/operating/managing the equipment or substance. That behavior is almost always coupled with pathological denials - both from the mutant super-idiots and their supposedly non-mutant peers.
2. General population humans are quite aware of problem #1, hence extremely distrustful when any human experts or organizations try to reassure them as to the safety of anything nuclear.
3. That "reprocessing" ain't nothing resembling "put on a lead apron and pour it through a coffee filter". Instead, it's a quagmire of chemicals and processes that'd still be horrific if nothing nuclear was involved, plus weapon proliferation overtones, plus all the problems noted in 1. and 2. above.