I don't understand this thinking. The only possible safety aspect is if for some reason the shooter did not clear the chamber or magazine and then the act of dry firing would clear the gun albeit with an AD. Provided the dry firing was carried out with the gun pointed down range I suppose it would be safer than inadvertently carrying and putting a loaded gun away.
However an AD would be totally unacceptable on any shooting range and the shooter would, or should be, heavily censured for that careless act.

In the world of clay target shooting shotguns must be carried open and empty at all times other than empty and closed while racked or loaded and closed when it is the shooters turn to shoot. At no time does anyone dry fire their shotgun, not that I have observed anyway after years of comp shooting. Shotguns remain cocked with the safety off as nobody wants to risk losing a bird because they left their safety on.

Dry firing a pistol after clearing the action and chamber achieves nothing safety wise because there must be a deliberate action later to insert a loaded mag and work the slide or charge the cylinder to load the gun when ready to use again.

Your club needs to re-evaluate that rule, I certainly wouldn't be dry firing a handgun without snap caps. Here in too lies a conundrum where a mix-up between snap caps and live ammo could occur especially if snap caps have been homemade on empty cases. Don't want another Alec Baldwin do we.