It's because you can dump lots and lots and lots of fossil fuel waste into the atmosphere for a long time before it starts becoming a noticeable health hazard -- and by then you can see it coming.
Radiation will kill you relatively quickly and you won't even know you're dying.
In 1952, 12,000 people died in a few days in the 1952 London Great Smog, caused by fossil fuel exhaust. In 1956, the world's first commercial nuclear plant went live at the Windscale/Sellafield site in the UK. The nuclear waste still stored at the Sellafield site may be scary, but it's not killing anybody; the fossil fuel waste very much did.
That's not the right comparison. The equivalent comparison would be, what if we just dumped nuclear waste out in an empty field, or in a river or something, or atomized it and pumped it into the air?
Radiation will kill you relatively quickly and you won't even know you're dying.