I grew up shooting a Webley 700 with automatic safety. I was always taught to treat a gun as if it were dangerous - safety on or off.
Since then I have owned and used guns with auto and non-auto safety and hammer guns with rebounding and non-rebounding locks.
Just treat the gun as if it were cocked all the time and periodically do a visual and manual check of the safety, like you periodically check the rear view mirror in your car.
Neither option is inherently safe or unsafe in my opinion, it is about the operator being disciplined in the operation of whatever he is using.
Of course, double rifles frequently have non-auto safeties because it would be pretty dangerous to load, close mount, swing and fire at a charging beastie - only to realise you left the saftey on. Then you are lunch!
