I don't mind people sitting on stones, but I'm sometimes bothered when I see folk standing on them. Not sure of my logic behind this, considering my arse has a larger surface area ;)
I therefore must think of them as the equivalent of a sofa, OK to sit on but keep your feet on the floor (r-e-s-p-e-c-t)

But I NEVER* stand on rock art. It can really do without it.

*as far as I know