In Robert Louis Stevenson's The Strange Case of Dr. Jekyll and Mr. Hyde the major conflict is the duality of man.
All human beings wear masks. There are emotions and capabilities within each and everyone of us. As social beings, we follow societal expectations by suppressing all that is instinctive and considered too innate. In front of others, we socially learn what is admitted or not accepted as propriety and we act accordingly.
The Strange Case of Dr. Jekyll and Mr. Hyde deals with the duality of our nature. Our main character suppresses certain behaviors only to set them lose with Mr. Hyde for the sake of experiencing in grandiosity all the sensations that he denies himself when he acts according to the gentleman's rules. Would it not be easier to live in a society that does not pass judgement upon the actions of others, or upon the uniqueness of some individuals? That may sound like a question with an easy answer, but Stevenson's times were times of extreme social scrutiny, hypocrisy, and elitist snobbery.
Hence, the ultimate message that Stevenson sends through The Strange Case of Dr. Jekyll and Mr. Hyde is that all people, rich or poor, have the same capability of lowering themselves to the depth of depravity for the sake of feeling liberated.
You have some valid points. However, be careful when giving the major conflict of the story. It is not the "duality of man" that serves as the story's major conflict, but rather the combined pivotal choices made by each character that stem from their dual nature. This distiction is very important to make when interpretting the story's "message" which is exactly "the duality of man."
On another note, as you've written "our main character" in the third paragraph of your answer, it appears from what you've written that you are referring to Jekyll/Hyde. I disagree with you on this matter and I'll quaintly say that Mr. Utterson is in fact the story's protagonist. Depending on what print you have of the story (some modern editions are quite rudely modified), this claim is or is not self-evident.
"Most [modern printings] omit the figure of Utterson, telling the story from Jekyll's and Hyde's viewpoint (as well as using the same actor for both roles)—thus eliminating entirely the mystery aspect of the true identity of Hyde, which was the story's twist ending and not the basic premise that it is today."¹