It's simple. Do not touch the rock art. Just leave it be. Earlier this year while visiting a rock art site open to the public not far from St George, where many pictographs are in open air on surface rocks facing the elements, there were a good number of people there enjoying the site. As I began to locate the petroglyphs just beyond an informative sign I observed a woman traipsing all over the rock art. I followed her patiently waiting for a clear photograph of the panels while carefully avoiding stepping on the graphics myself, all the while shooting scowls her direction. I perceived that she began to take a little notice of the respect I was giving to each element I found in her wake. Yet as she stood on another nearby panel while photographing younger family members who were standing on yet another rock art laden surface I heard her exclaim "I can't believe they let you walk all over the rock art here".
No, they do not let you walk all over the rock art there. They let you view the rock art up close without fencing you off or otherwise putting you on a leash there and they let you do so on your best behavior. Her statement seems to indicate she was basically aware that not to be walking all over the rock art was better for the rock art, but her actions betrayed her ability to act on that knowledge. Perhaps so conditioned by sites that are fenced off that having no restriction lead to some confusion? To be fair, some of the rock art there can be hard to spot for the novice site visitor or general public, the sun glinting off the rock surface and the patination of some of the older elements help them blend in well, she may not have spotted some before stepping on them. But somehow the message on signs at the site were not read, not understood, or somehow didn't impact the person enough to quite modify the behavior of that visitor, at least up to that point. I hope my example, more than my crusty looks her way, helped it begin to gel a little.
Educate yourself and your family when you visit such sites, notice the carsonite markers and information kiosks and follow the easy instructions printed on them. Teach your family and friends in your party proper site etiquette, that way should you happen across sites in the wild that are not prepared for public visitation your party won't be "those people" who ruined the site for everybody else. "Don't touch"! It's simple.
A don't touch sign at another location, Mckee Spring petroglyph site, September 2006.