I'm of the opinion that nuclear reactors are generally safe when good engineering and operational practices are adhered to, and do understand that they're a reliable, significant power source.
The main two issues which lead me away from nuclear at the moment are:
- Externalities: even though I've read about various ways to store/dispose of nuclear waste long-term, I've yet to hear of a solution that seems clearly safe -- especially compared to the alternative of not producing nuclear waste in the first place.
- Cost: From what I've seen, Levelized Cost of Energy (LCOE) seems a standard measure for overall cost of energy production by source, and as of relatively recently, it seems that wind and solar are generally[0] now cheaper than nuclear.
If it's cheaper and externality-free to pursue renewables, that seems like a pretty strong anti-nuclear argument.
I'd agree there's also a larger real-world audience to convince one way or the other -- but I'd also be wary that they'll accept equally spurious arguments about wind/solar not being workable.
I think brief 'talking points' end up being pushed by industry a lot to try to influence people in one way or another - and that those end up flowing through communities and social networks and defining people's 'default' reaction in debates based on cherry-picked arguments even if they haven't had time to read further about the issues.
[0] - https://en.wikipedia.org/wiki/Cost_of_electricity_by_source