This could very well be for insurance reasons - it may be a requirement in their policy to keep spectators at a specific distance.
some other issues:
1. as reenactors, we have all signed waivers regarding any accidents/injury. The public typically does not (unless printed on the tickets as they do with sporting events)
2. as far as artillery, one reason we need a clear area is primers. When we fire the gun, the primer takes off like a bottle rocket. We did a reenactment where we had a cannon on a stern wheeler on the Ohio river. we were as far forward as we could get, and we found spent primers at the stern of the boat. Also, our limber box will have quite a bit of powder. while not likely, we need a safe area around us just in case there was an accident with the limber.