What does it mean that Mr. Utterson says he inclines to Cain's heresy in his dealings with others?
Although The Strange Case of Dr. Jekyll and Mr. Hyde by Robert Louis Stevenson is best known for its protagonist, the doctor who manages to separate his good and bad natures off from one another by a mysterious potion, the narrator of the story, Gabriel John Utterson, is in some ways just as interesting a character.
Stevenson himself was raised a Calvinist, and though he abandoned his early interest in religion and became an atheist, strong religious overtones still permeate this work. In a sense, while Mr. Hyde represents sins of commission, Mr. Utterson represents sins of omission. In other words, Mr. Hyde does many evil acts, but Utterson stands by and lets evil things happen which he might have been able to prevent had he abandoned his stance of neutral, objective curiosity. In many ways, Utterson's moral failings are those which we now consider the virtues of the scientist or journalist or lawyer (his actual profession), of objective neutrality. Like Jekyll/Hyde, Utterson too is a doubled character. His professional persona's strength is his calm, nonjudgmental objectivity and ability to stand outside the events he observes; his human persona is capable of sympathy and moral discernment, and often stands by staunchly even those of whom other despair. While the protagonist Jekyll/Hyde disintegrates in trying to separate these two parts of himself, Utterson gradually increases in self-awareness and begins to integrate his two natures.
The "sin of Cain" is, as noted in the other answers, an unwillingness to get involved or take action. Unlike the "good Samaritan" who feels obliged to care for others, Cain asks "Am I my brother's keeper?" disclaiming all responsibility for other people. Thus Utterson is described as follows:
"I incline to Cain's heresy," he used to say quaintly: "I let my brother go to the devil in his own way."
By the end of the novel, we begin to understand that at times intervention is necessary. For example, if you see one of your classmates about to drive when drunk, you should take away the classmate's keys. If you let the classmate drive drunk, you are morally, if not legally, culpable if the classmate injures herself or others. Moral goodness, Stevenson is arguing, depends upon being one's bother's keeper.
On the first page of "The Strange Case of Dr. Jekyll and Mr. Hyde" Mr. Utterson the lawyer is quoted as saying:
"I incline to Cain's heresy. . . . I let my brother go to the devil in his own way."
In the Bible when God asks Cain where his brother Abel is, Cain answers, "Am I my brother's keeper?" This could be called heresy because God and the Church expect people to be concerned about their brother men. But Utterson is in the habit of telling people that he lets his brother men do whatever they please without being concerned or curious about them. He had very few close friends. He did, however, become concerned about Dr. Jekyll because the good doctor seemed to be under the influence of an evil-looking character called Mr. Hyde. Utterson also felt responsible because he was Jekyll's executor and his lawyer. It was for these reasons that Utterson became so deeply involved with what Stevenson calls the "case" of Dr. Jekyll and Mr. Hyde, suggesting that it is a complicated legal case with complex ramifications involving such things as possible insanity, murder, suicide, extortion, false impersonation, and fraud.
In simpler terms, Mr. Utterson is basically saying that he sides with what Cain, the brother of Abel, said to God when He asked him where was his brother. Cain, who is known for being insubordinate, also epitomizes "bad blood" because his answer to God was basically "what do I care where my brother is...am I in charge of him?"
Am I my brother's keeper?
Back to the novel, Utterson uses Cain's statement to indicate that he, too, has little to do with what other people do; that he only minds about himself and his own business.
I let my brother go to the devil in his own way.
These words are a refined way to say that, for all he cares, people can do whatever they want, and that he does not care.
Yet, we know that Utterson does care. He cares enough to want to get to the bottom of what is going with Dr. Jekyll, not only at a business level but also at a personal level. He consistently tries to correlate the influence of Mr. Hyde and wants to know how he can change whatever is coming Dr. Jekyll's way.
Cain's heresy is the reply he makes to God, when God asks the whereabouts of his brother Able. Cain's answer, "Am I my brother's keeper?" is one of the most well known quotes in the world. Utterson deems it a heresy because, to deny responsibility for one another, especially one's brother, is the antithesis of everything taught in the Bible.
When Utterson utters his spin on the phrase - "I let my brother go to the devil in his own way" - he casually dismisses 2000 years of Christian morality and ethics, prefiguring the modern existentialist movement. The rise of the crowded, chaotic, industrial city, the London of the novel, lead to a fragmentation of life that hadn't been known by people raised in small rural towns. This detachment from caring about the lives of those around you finds to its logical conclusion in Camus' "The Stranger," where the narrator, Meursault, kills a man without feeling any guilt or remorse. He declares that God and the universe are indifferent to the meaningless actions of human beings.
Utterson, however, is not such an extreme existentialist, and becomes intimately involved in the strange circumstances of Jekyll's life, mostly because of his position as Jekyll's lawyer. Caring about one's fellow man, then, in the novel, is based not on any moral responsibility, but on financial, or employment responsibility. By following through with that duty, becoming involved in his life, Utterson comes to genuinely care about Dr. Jekyll.