Does radioactivity becomes more hazardous once we've touched it?

Of course not. Radioactivity is radioactivity (of the various varieties there is of course) whether it's just lying in ground for 2 billions, or whether we dig it up and manufacture some fuel rods out of it.

So then what is this neurotic obsession with radioactive material, that was lying in the ground, once it is extracted?

Timmy makes a good observation.

Further, think about what the actual complaint is even if it does leak. There
used to be lots of uranium in the ground here. Now some of it has gone back into
the ground. Scary, eh?

Once we take some uranium out of the ground, what's wrong with allowing it seep back in? It was already there in the first place!

It's like the epic tale of 10ft metal pipe. A nuclear operator orders 10ft of metal pipe. As with all materials, there is some natural radioactivity in this pipe. The technicians get the pipe, but only need to use 9ft of it. The remaining 1ft is scrap. However, because of this natural radioactivity, the pipe must be treated as low level waste. Can't see a coal fired power station being particularly bothered about that.

This highlights more stupidity about waste arguments. Best one is depleted uranium and the outrage that opponents display towards the buildup of this EEvil substance. We take natural uranium out of the ground, which has a specific activity of 12.8 MBq.kg^-1* and return it as depleted uranium, which has a specific activity of 12.3 MBq.kg^-1. In doing so, we've made the ground less radioactive. Surely the radiophobes should like that. But because the radioactivity is something that we've touched, it automatically becomes worse than what was sitting in the ground naturally.

On nuclear waste as a whole. By disposing of vitrified fission products, which will decay to below the activity of uranium ore within 600 years, the legacy we are actually leaving for future generations is a ground, which is less radioactive in the long term than it would be otherwise.

Think about that!

*Figures are in becquerels per kilogram of uranium, ignoring all the other stuff in the ore.