Part of the reason I want my dogs to wait or not rush the door is safety - it's not necessarily that I don't want them going in front of me, but I don't want them to think it's okay to come flying through an open door past me. Even though my dogs could always tell the difference between the back door and front door, it seems safer to just have a dog thing that it's unacceptable to rush through a door like that.
Plus...not that I mind them going out first...if I step aside and tell them to, but if I'm going to go through a door, I don't want some dog rushing past me and practically tripping me or slamming into my legs or pushing the door further open. Or standing in my way scratching or panting or whatever right in front of the door while I'm trying to open it.
I wouldn't be ok with another person doing that, because it's just rude and annoying, and I don't feel any differently about a dog doing it.
If other people aren't bothered by it, go ahead and let them do it. But personally if I had to deal with that every time I had to go outside with my dogs, or let the dogs out, it'd drive me nuts.