I was going 'where the fuck did that come from?' and then I looked it up:
A) no fucking wonder and B) that's honestly really cool I'd love to go there. With a dosimeter and a Geiger counter and some extra PPE. I'm a radiation professional, it would be fine.
The radioactive trash is glow-in-the-dark deck markers from old ships that kept sailors from falling overboard in the dark - two of them were found on the beach, and, more concerningly, they've leaked and contaminated the soil around them.
Some people are debating whether this really constitutes a significant hazard, and I have to agree that I've got doubts, although I can't be very confident one way or the other without knowing how much radium is in the things. If the radium was still contained I'd be less worried, but one of the things that makes items like radium watches fairly safe is that they do stay contained. Breaking one, as these deck markers have been broken, is more risky.
I understand why the NPS didn't want to be responsible for what might happen if the public got its hands on these things. I wouldn't want that on my head, either. It's probably not too dangerous with appropriate precautions, but the public cannot be universally relied upon to take precautions. The nightmare scenario would be someone managing to ingest high levels of radium, perhaps by handling a broken deck marker and then eating with contaminated hands.
To a radiation safety professional, that immediately brings to mind the Goiana incident - which killed several people. That was a scarier source, but this is far from safe. I'd also be worried about accidental injection of radium if anybody got cut on contaminated glass. On the broken glass beach.
The thing about radium is if it gets in your body, it sticks around. It likes to mimic calcium and get into your bones. Radioactive artifacts like this aren't super harmful outside the body, when they're sealed, but internal contamination could be really nasty.
Wait, 2005?! 20 years? This doesn't actually sound that hard to clean up, but - oh. I bet it's a funding thing. It's the NPS and rad waste disposal is expensive as fuck. So is the expertise and equipment you'd need for that type of project. And then you'd have to worry about whether there might be more than the 2 discovered sources in there - because it's Ra226, most of the radiation would be blocked if anything was buried under the rest of the trash. And the terrain (broken glass) is horrible for the bulkier and more sensitive types of detectors, too.
Yeah, they're really not fixing this anytime soon, are they? That's a mess.