I'm still not sure what exactly triggers it but you're able to explore almost all of New Austin as Arthur in chapter 4. I think you can only do this after the Fatherhood And Other Dreams - II mission, the one with Mary Linton . After you complete the mission you can cross the border without the bounty hunters spawning or getting shot at. I've noticed that once you're across the border the wild life will be more aggressive in their attempts to kill you and more of them will spawn. If you get caught doing anything illegal or cause any commotion the bounty hunters will instantly spawn around you and almost instantly gun you down. If you die you'll spawn outside the border at Montana River, no matter how far west you are.As Arthur I've talked to Herbert Moon but Arthur didn't ask about the Strange Man picture like John did. I've also went to the location where the Strange Man is on RDR1 as Arthur to see if he'd be there, no luck. I explored most of New Austin hoping that I could find Mary Linton so Arthur can get his happy ending and live. Another thing I went to get as Arthur was the ancient necklace that the blind man hints to in his riddle about the black flower, but so far it hasn't done much.I accidentally figured this out on my first play through of the game when I was hunting the legendary animals. I just gave it shot on how far I could make it and noticed that no one bothered me. I didn't think much of it at the time and actually did get the Legendary Bison, Cougar, and (I think) Elk. I tried to go back later on in the story to get the plants for the herbalist challenge but was getting shot down again by the bounty hunters and had to wait until I was John to go back. I was wondering why I was able to go in a certain part of the story and not the other, so I reloaded a save that was in Chapter 3 and kept doing missions until I was able to go back in as Arthur.Anyways you guys can give it a shot and tell me if you figure anything out. I was hoping I'd be able to post an awesome easter egg for you guys but I haven't found much

EDIT: I think I've figured out the exact steps to do this. In the Angelo Bronte mission where you're looking for grave robbers you have to be seen by the police and then escape (don't sneak around). Once you've escaped finish the mission as usual, then go to the post office and pay off the bounty. From there you should be free to explore New Austin. Here's a clip of me doing it - https://youtu.be/2zUDmjOHHx0

EDIT: Just another clip https://www.youtube.com/watch?v=QTbEsiJhrBk

EDIT: Like Retrash has said you can do this trick any time after finishing the mission by replaying it. Just have to pause the game - Progress - Story - Chapter 4 - Angelo Bronte, a Man of Honor. This way you don't have to pay the bounty off and if you missed it you can always go back. Here's a clip for an example https://www.youtube.com/watch?v=EAUVjA_8yCg I cant make my vids more than 15 minutes long and can't really edit them but you get the point