We did a lot of walking last week. And I found myself carrying my rifle on my right shoulder muzzle forward only if everybody was to my direct left. and muzzle rearward if I was last in line. At other times/positions I appear to be deeply psychologicaly programmed to be incapable of doing so. The muzzle must point upward and away from anyone.
Last year I did carry my double for 5 days in the AC position, however it was broken. Again this is I think from years of conditioning hunting birds in company. Never felt that it slows me down as closing the gun and releasing the safety is again deeply programmed.
I have seen a loaded double fall from a shoulder and discharge in a stumble, all be it a shotgun. That was to a very experienced shooter, and another slip on a seat with the same result.

I don't think that there is a right or wrong answer to this, but I would not walk in front of somebody carrying in this manner.

Regards