there is the (albeit possibly slim) chance of you breathing in the dust, thereby getting non-degradable radioactive material into your lungs, with all that entails.
If museums buy a Geiger counter, and supply visitors with dust-proof sprayers’ masks and over-suits, which can be destroyed after use, maybe 100% access might be regained, but don’t hold your breath.

Hmm.. DO hold your breath. That’d also work.