Well, this is where maturity comes into play, and common sense too.
To me, having a loaded airsoft gun isn't a big deal, some people just need to be trained on proper "weapon" handling. I've heard the arguement, "but its not real, who cares", this is the wrong attitude. I walk around on a regular basis with a loaded automatic weapon(or several on my guntruck), so weapon safety and handling is second nature. Anyone who has sufficient amount of time around firearms knows about muzzle awareness. A few tips to keep safety from being an issue.
A.) Get a good sling. If you don't have to touch your weapon, and you can still have good control over it, you'll be good to go. I see to many people holding their rifle by the grip, arms danging at their sides.
B.) Get some ballistic rated sunglasses and some goggles to go over them, if you are REQUIRED to have sealed eyepro. I highly recommend Oakley M-Frames for the sunglasses, don't cheap out on stuff like this. I've had mine for a while now, and they have minimal scratching, and I can wear them for hours on end without becoming uncomfortable. For sealed eyepro, I recommend the ESS Land Ops, or NVG Profiles. I've used both here in highly dusty conditions, and I was completely comfortable wearing them over my Oakleys. After the game, take off the sealed eyepro, and you still have some ballistic protection if a BB were to somehow hit you in the eye.
C.) Make sure you have your shit on safe when you come back into the staging area. If you need to, have someone walk around and check. Some people worry about magazines in the weapon, but I personally don't see it being a big deal provided the weapon is on safe, and proper weapons handling is being excerised.
On the safety briefs, I agree, for the most part. At larger games they should be essential. Some of the smaller games I've gone to with my friends that I play with on a regular basis, its not an issue. Test fire zones should be designated, a safety word, or signal should be designated so if someone gets hurt, everyone knows whats going on(I know we've done this in the past). If someone violates a simple rule, you could be a dick and tell them to leave, or be someone nice about it, and tell them they have to sit out.