That's the trouble with radioactive isotopes. A hundred thousand years is long enough that it will be radioactive for longer than we can foresee, many times longer than written history, but it's short enough that it's still very active. Even a gram will have billions of decays per second. And while our body is of course capable of repairing a small amount of DNA damage, evolution never prepared us for a continuous bombardement by the subatomic equivalent of a machine gun.

Pu-239 [0] has a half-life of 24k years, and is considered dangerously radioactive.

Of course, this only applies when we're talking about large quantities, like radioactive waste. I have had a bone scintigraphy done, which means I probably have a fraction of a gram of Tc-99 with a half life of 211k years embedded in my bones, which is unlikely to be an issue. But I wouldn't want to store a decent chunk of that under my bed. I would, however, have no qualms about sleeping with uranium 238, an alpha-emitter that lasts many billion years.

0: https://en.wikipedia.org/wiki/Plutonium-239#Hazards

Why are we talking about 100,000 years, when all we know with any confidence is that things will be so different in 100 that it is impossible to predict most of the problems that will face us then?

In fact I have trouble imagining a future where people still exist, but this problem is not solved or obviated well before 100,000 years from now -- in fact before 100.