100% safe is never the metric. Nothing is 100% safe. Every form of energy generation has risks that have to balance the good the energy source brings. Nuclear is nearly unique in that it can produce carbon-free energy (unlike fossil and biomass), continuously for 2 years on end between reloads (unlike wind/solar/coal), and it can be deployed in a wide variety of geographic locations (unlike hydro and geothermal).
The risk is that there are occasionally nuclear accidents: Three mile island and fermi 1 meltdowns, both of which killed zero people. Chernobyl, which killed ~50 from ARS and up to 4,000 early deaths over the next several decades (on top of a few million cancers that would have happened anyway in the population). Fukushima, which killed up to one person. Can anyone name any fatal natural gas explosions? Any hydro dam failures that killed 100,000? How many people per year does coal kill by operating normally (~200,000). We as a society accept certain risks from our energy infrastructure because of all the good we get from it.
Here is a plot of how many thousands of days of life are lost by various things [1]. Note that nuclear is almost ridiculously low. This chart doesn't include the impact of climate change on human lives. Nuclear fission is a climate superpower, and we cannot be justified in neglecting this natural resource because we're afraid of something going boom.
TLDR: A factor of 100x improvement in nuclear safety goes from tiny risk to supertiny. Current plants are already safer than almost everything else we know. Some studies have more people dying from installing solar on their roofs than getting killed by radiation from nuclear fission plants.
[1] https://i.imgur.com/ClgbpA4.png