As above, muzzle awareness is everything. It's hard enough for newcomers to remember everything and all too easy to get confused by muzzle up/down, in or out of a slip etc etc....just using common sense and muzzle awareness at all times gets, or should get you to the right way of doing things. I rarely, if ever carry a rifle muzzle down, especially if loaded. The risk of a discharge, for whatever reason (negligence or not) ricocheting and causing injury is too high, especially over hard ground. That's my reasoning anyway plus I prefer longer barrels, weight penalty or not, so the risk of scraping and damaging a mod or barrel is also too high.
I always carry a rifle muzzle up for those reasons, ensuring that the muzzle is up and not slipping back to a dangerous slant, as I've seen numerous times when following others, their barrels slipping back an almost pointing at the person immediately behind them. When unloading, the rifle is pointed at the nearest backstop (ie it's always done before leaving the field and never when I get to the back of the car) and often, the mag is removed and stored at that point.
With shotguns, I carry barrels up (I rough shoot alone and am not with anyone else) as I find bringing the gun to the shoulder a lot quicker that way. It stays barrels up within the slip as well. I just make sure that I have a decent slip with decent zip and fastenings and have never in 35 years had a gun drop from the slip.