Sure, reactor design has changed since Chernobyl in various ways that help mitigate it, but what about Fukushima?
Fukushima was devastating, and the result was the NRC asking US reactors to reconfirm their flooding and earthquake preparedness. I don't know of any measures taken in European countries.
As climate change progresses, there could be some disastrous consequences, and it's unfair to say that the skepticism is outdated.
This isn't to say that nuclear is worse than coal (it's not), but that it isn't just handwaving.
You don't have a baseline energy with wind and solar, which are not on-demand. That's the big issue.
And nuclear _can_ be cheap if (and only if) funded by states, that can borrow zero-interest loans.