If you're smart, and careful and plan well and don't try to cut corners, you'll be safe.
Chernobyl was hampered by design flaws [1] that can be pretty well avoided these days, and it's not like light water reactors are the only / best option, either.
Right or wrong, people aren't worried about design flaws that are known about, it's the design flaws that aren't anticipated. There's plenty of safely operated nuclear energy facilities, but the prospect of one contaminating either a large urban area or a large agricultural area is pretty horrific. I suspect most people aren't worried that the theory and design of new plants is safe, but that the practice wouldn't result in at least one plant with corners cut.
I'm personally comfortable with the idea of nuclear power, but I don't really begrudge people who aren't too much. It's all moot anyway; for providing base load, natural gas is going to be the hands down winner for awhile. I could be mistaken on this point, but I'm under the impression that they're both cheaper and faster to get going, and easier to decommission.
Isn't hindsight great? I suspect the people who designed Chernobyl thought they were being smart and careful at the time.
You can be as smart and careful as you like, and still get bitten by something you had no idea was a possibility. If you're building a wind turbine, there's likely to be a reasonable limit to how catastrophic that totally unanticipated problem might be. If you're building a nuclear plant, the stakes are a lot higher.
I'm personally comfortable with the idea of nuclear power, but I don't really begrudge people who aren't too much. It's all moot anyway; for providing base load, natural gas is going to be the hands down winner for awhile. I could be mistaken on this point, but I'm under the impression that they're both cheaper and faster to get going, and easier to decommission.