I believe that Mr. Raymond does this because he wants to live by his own values (he does not want to give in to what society says) but, at the same time, he does care to some extent about other people's feelings and opinions.
If Mr. Raymond truly did not care, he could just say "hell with 'em." He could be more in your face (as we say today) about his life and not care about what others thought. But he does care some about the other people's feelings. So he tries to give them a way to rationalize his behavior. He tries to let them feel that he only goes against society's values because he is drunk.
So Mr. Raymond is not a complete rebel. He does act in a very rebellious way, but he still cares about the feelings of the people in the community.
You can see evidence of this early in Chapter 20.
In To Kill a Mockingbird, Dolphus Raymond is a fairly simple man who's just trying to live life in the way he chooses. Unfortunately, he's chosen to mingle his life with the negro culture--a definite taboo in his time and place. The culture in Maycomb is such that black is black and white is white, and never the twain shall meet. Dolphus was engaged to a white woman who committed suicide when she discovered he was continuing an affair with a black woman. From that point on, Dolphus spent his life on the outskirts of town, the only place available to him. He has "mixed" children, and they, too, are ostracized. He carries a brown paper bag with a beverage in it to help others try to explain what, to them, is unexplainable. They can not understand his affinity for living with black people; if they think he's a drunkard--and therefore not in total control of his faculties--they can more easily explain and justify to themselves his inexplicable lifestyle choices. His beverage of choice is actually coca cola, of course, but he lets everyone think he's a drunkard to help them cope rather than save his own already tarnished reputation.