The problem is that anything involving the word 'radioactive' is heavily overladen with emotional angst, when other similarly dangerous things are not.
some scepticism  is perhaps justifiable considering the appalling effects of over exposure of national servicemen and the local populous  in the 1950s, when the attitude was more gung ho. (https://www.justsecurity.org/56127/devastating-legacy-british-american-nuclear-testing-kiritimati-christmas-malden-islands/ )

However, the problem is that to attempt to reduce all exposure to natural levels is very much over engineering - the very lowest level nuclear waste is probably less radioactive than many naturally occurring minerals.  The other unknown is one of inadvertent concentration - does a certain plant or animal ingest and then accumulate radioactive material re-concentrating it from the dilute into something more concentrated and dangerous? Humans do in the thyroid, hence iodine tablets which suppress this effect. As longer studies are possible in  places like the area around Chernobyl occur, this sort of thing is far better understood than it was last century.

In practice there is not a huge amount of really dangerous waste and there are ways of storing it that we can be pretty confident about. I'd not be too worried about  it, but then I'm a professional  whose career is grounded in the physics.
Mike

Note as an example that the reason our nuclear subs are so expensive to decommission is not that the original builders had no plan - on the contrary, they expected them to be towed out to sea, pumped full of concrete and sunk in deep enough water not to be disturbed. This is no longer considered as acceptable

The problem is that anything involving the word 'radioactive' is heavily overladen with emotional angst, when other similarly dangerous things are not.
some scepticism  is perhaps justifiable considering the appalling effects of over exposure of national servicemen and the local populous  in the 1950s, when the attitude was more gung ho. (https://www.justsecurity.org/56127/devastating-legacy-british-american-nuclear-testing-kiritimati-christmas-malden-islands/ )

However, the problem is that to attempt to reduce all exposure to natural levels is very much over engineering - the very lowest level nuclear waste is probably less radioactive than many naturally occurring minerals.  The other unknown is one of inadvertent concentration - does a certain plant or animal ingest and then accumulate radioactive material re-concentrating it from the dilute into something more concentrated and dangerous? Humans do in the thyroid, hence iodine tablets which suppress this effect. As longer studies are possible in  places like the area around Chernobyl occur, this sort of thing is far better understood than it was last century.

In practice there is not a huge amount of really dangerous waste and there are ways of storing it that we can be pretty confident about. I'd not be too worried about  it, but then I'm a professional  whose career is grounded in the physics.
Mike

Note as an example that the reason our nuclear subs are so expensive to decommission is not that the original builders had no plan - on the contrary, they expected them to be towed out to sea, pumped full of concrete and sunk in deep enough water not to be disturbed. This is no longer considered as acceptable