I don't think most people do. Well, there is the usual NIMBYism, but the energy industry has figured out how to rally the public, even if it is for something disastrous like fracking.
I think the *idea* that most decision-makers and advocates are against nuclear because of those two reasons (waste & explosion), is holding us back from having a constructive conversation.
Just my 2 cents, I haven't done any academic work on this.