For what it's worth, most of those JSO protests have been done in a way that would not damage the actual object. Like the Stonehenge one, it wasn't paint, it was cornflour and food colouring that would just come off in the rain (and was, in the end, removed with just a leafblower). The Magna Carta one actually was doing damage though.
Regardless of that, I don't personally think that they are effective protests. They're far too easy to frame as mindless vandalism.
I'd hate for future generations to miss out on seeing those things. It sure would be a shame for fires, floods, storms, or mass die-offs to spoil that.
What's the point in preserving history if there's no guarantee of a future?
They didn't call themselves People for the Gentle Handing of Historical Artifacts and they have yet to destroy or murder a single thing they've claimed to be interested in protecting...
Given the backlash against environmental protestors blocking traffic, can you imagine the backlash against the oil industry when an unusually severe storm or flood or landslide blocks traffic?!