Sounds as though someone is being a bit precious.
If the public are off the airfield it is up to the pilot not ATC to decide whether to continue the approach. I assume that the Reds do not often land short of the runway, so the risk is low.
If these people choose to ignore clear signs stating the potential danger, it is their decision. Clearly, if their actions distract the pilot, an overshoot should be initiated.
I do remember the good old days at Valley when ATC would request one of the 3 Sqn Hunters to move the spotters from the fence or rock outcrop on the RW14 approach. With students doing PFLs and 1in1s the undershoot was definitely not a safe place to be!