To take Richard Gere's character, Billy the Kid, as an example, he was free to live his life as he wanted, so long as he stayed clear of the public eye and their influence. He lived unaffected by society because he chose to do so. One could make the argument that Bob Dylan also tried to live part of his life that way, so as to not be too affected by society, and to have freedom to write about what he wished.
Cate Blanchett's character, Jude Quinn, could be a good example of how Bob Dylan tried to live his life in the eyes of the public. Quinn was constantly under the scrutiny of the public. Everything he said or did was placed under a microscope. Nevertheless, Quinn gave himself his own freedom to say and do whatever he pleased. Was it director Todd Haynes intention to use these characters as the different sides of Bob Dylan? You'd have to ask him.