On top of what @_MT_ said, the other problem with Chernobyl was its management. The problem only occurred because they had safeties disabled for testing and ignored the warnings. If they had proper protocols in place, and had used them, it never would have happened. And the sickness and death it caused would have been significantly less had the government immediately admitted what had happened and evacuated the area, but they tried to cover it up.
The military has been using nuclear reactors for half a century plus, without incident. There have been only a couple other incidents of note, and only one (Fukushima) had real consequences, and those have been relatively minor. And as _MT_ said, we have the knowledge and technology to build them so much better than the ones we've been using, which have already done incredibly well. But, as he also said, people are generally vastly misinformed, because they don't bother to do their research and simply say things they've heard or believe, instead of what's real. For example, years ago, I read a comment by somebody saying reactors are unsafe because somebody can just shoot one with a .50-cal. Reactor domes are designed to withstand the impact of a 747, and reactors generally have high security. But why let the facts get in the way?
_MT_ also mentioned that the waste is still a rich fuel, which is true. The only reason we have so much nuclear waste is because people complain about nuclear reactors and the waste they create and so don't want new ones built, so the waste sits around instead of being used in a breeder reactor, which would reduce the current waste to something like 1%. Meanwhile, some countries have figured this all out, and one European country (France, I think) generates so much nuclear power they export a lot of it to surrounding countries, so they're generating GDP from it.
And the thing I really don't get about all this is that it's typically the same people that complain about global warming and say the world is going to end soon if we don't take drastic action that are the most against nuclear power. They'd rather a near-guaranteed, slow death of the planet than the implementation of a technology that would solve the problem almost immediately, just because it might have disastrous, mostly local, consequences, even though the risk of that is extremely low based on our history with and knowledge of the technology.
But then, those same people believe a certain action should be legal because their body, their choice, yet that people shouldn't have a choice about another action being performed on their bodies. So logic clearly isn't at play here.
If you want to be anti-nuclear, that's fine, but at least educate yourself on it first.