The biggest problem with adoption of nuclear energy is trust
When people argue against nuclear energy, it all comes down to a single common problem. Lack of trust. At its worst, we know that nuclear energy can kill lots of people very quickly. We know that nuclear radiation can cause fatal sickness over time. We also know that we have effective ways of controlling and containing nuclear energy. So keeping nuclear safe is not a question of know-how.
When someone asks, "What about the waste?" they may not realize that cooling pools and dry caskets resolve the issue completely. Also, keeping the "waste" relatively handy allows us to reprocess it into additional fuel. The "waste" is a resource. Instead, they believe the companies and governmental agencies overseeing nuclear operations will take the "cheap and easy" approach of dumping the waste in landfills and our water supply. Perhaps there is some history of bad behavior, so the assertion is far from crazy.
When someone screams, "What about bombs?" they are expressing distrust in bad actors (individuals and nations) who would use the bi-products of fission, such as plutonium, to build themselves some mutually assured destruction. Or for bad actors with fewer resources, the radioactive waste could be fashioned into dirty bombs that scatter slow death over large populations. Okay, I suppose we can agree these outcomes are possible. Bad actors can also do their nasty deeds with gasoline and a book of matches, or a truck full of fertilizer. It's not much different.
When someone says, "What about accidents?" they are expressing a lack of trust in the people and systems who keep nuclear working safely. Humanity's track record in nuclear demonstrates decades of incident-free operations, with a few notorious pock marks. Three Mile Island, Chernobyl, Fukushima. Is that it? While the possibility of more accidents is non-zero, what we have learned makes them less and less likely.
When someone says, "What about the cost?" they are weary of the price tag for constructing such enormous steamy beasts with all of their safety controls. They may also understand the tendency for people to pad budgets in order to line their pockets with public funds. The cost of building in safeguards that prevent accidents is worth it. We wouldn't want to skimp on safety. But how do we find the right line between enough and overpaying? Only with practice and experience and, if we allow it, a healthy dose of market competition.
So at the heart of the push back is an understandable lack of trust.
My hypothesis is that building trust starts with understanding facts about how things work. Teach people about physics, engineering, safety systems, the fuel life cycle (from mining through use, reuse, and eventual long-term storage), and research into better approaches. Share anecdotes of people living and working in harmony with nuclear. Contrast nuclear with other options from an even-handed perspective. When more people can think about nuclear without their hair catching fire, we will have a better chance of making progress.
Once we clear out the proxy reasons for objecting to nuclear, we will be left with our trust issues. I am not sure we humans will ever resolve our trust issues, but we can keep the lights on while we try.