Dolphus allows people to think of him as a drunk and a miscreant to draw attention from the fact that his real "crime" as they might see it, is his relationship with a black woman.
This allows townspeople to excuse his black mistress, and they chalk it up to his drinking.
I know this question was asked years ago, but I'd like to improve on the answer for others viewing this question in the future:
Dolphus Raymond did not make himself into an outcast to "distract" Maycomb from his black mistress (I might add to the persons who suggested this that she WAS his mistress when he was engaged to the white woman, but at present she is his WIFE). Rather, quite cleverly, he let himself become known as a drunkard under false pretences in order to free himself from their criticism. The people of Maycomb can't accept that he WANTS to live with the Negroes so he gives them the convenient excuse of his "drunkenness" as seen in the following quotation-
“When I come to town … if I weave a little and drink out of this sack, folks can say Dolphus Raymond’s in the clutches of whiskey – that’s why he won’t change his ways.”
He doesn't care that people know about his wife, he isn't trying to distract them, he's just saving THEM the trouble of complaining and HIMSELF the trouble of arguing. Furthermore, since he doesn't live in town it's not much of a bother to him. In fact, it's convenient. When he needs to come into town nobody talks to him, he can just go about his business and then get out-- back to where he prefers to be.
Like Calpurnia’s speaking one language at home with the Finches and another at the African-American Church, Dolphus Raymond’s double life shows Scout the compromises people have to make in order to live in communities where they don’t quite fit in.
Dolphus Raymond mad himself into a town outcast to distract the people of Maycomb from his marriage of a black woman. Instead of being known for his marriage, he is known for being a drunk.
He doesn't want people to know that he had kept a black woman as his mistress. Actually, he comes from a very good white family but he has to go so low to find desire and fulfillment from his black mistress. His white mistress even got pregnant and give birth to children, so it is right to say that she is her second wife. In fact, his white wife hadn't make a official divorce with him, so he was still legally married. So, Dolphus Raymond had actually committed bigamy, which is a serious offense and against the law of conduct. Like Mayell Ewell kissing Tom Robinson, which is a serious offense as a white woman had tempted a black negro, he had committed a much serious offense than this as he had even make a Negro pregnant, which is implorable.
So, as to hide this dark side of his, he had to cover up all loopholes and hide the truth to the Maycomb citizens as his reputation may crumble down to pieces if his terrible act had spread around. He had deceived his fellow citizens by tricking them to believe that the drink inside the bag was whiskey, making people believe that he is a lowly drunkard, but actually it was just plain old Coca- Cola. It turns out that Raymond has taken the psychological pulse of the town and had realized that:
"they could never, never understand that I live like I do because that's the way I want to live"
If the town believes that he does it because he is drunk, then they will shrug their shoulders and leave him alone, so they won't keep on questioning on his past life and he won't have a hard time explaining his own decisions. He would have a "peace of mind" and he can mind his own business, without bothering to defend and argued for his own actions. Better be known as a town drunkard than a negro-lover!