The conflict of "The Bride Comes to Yellow Sky" is best identified as Human versus Self. The Marshall goes to San Antonio to see a woman he has either met on an earlier trip or has heard of:
[he] had gone to San Antonio to meet a girl he believed he loved,
Potter, the Marshall, knows that society does not allow for secret marriages, especially when there are many friends to be consulted and confided in and, even more importantly, public officials to consult and confide in; secret marriages were looked on with serious disfavor:
[he] induced her to marry him, without consulting Yellow Sky for any part of the transaction.
The Marshall knows that Yellow Sky looks up to him and depends upon him, thus his actions weigh heavily toward their happiness. As the town friend and protector, he feels his duty toward them in a particularly serious vein:
people in Yellow Sky married as it pleased them ...; but such was Potter's thought of his duty to his friends, or of their idea of his duty, ... [that] he felt he was heinous. [...]
A sense of mutual guilt invaded their minds and developed a finer tenderness. They looked at each other with eyes softly aglow. ... The traitor to the feelings of Yellow Sky narrowly watched the speeding landscape.
Though the Marshall knows all these things about Yellow Sky, he cannot bring himself to stop and act in accord with what he knows in his conflict with himself:
Frequently he had reflected on the advisability of telling them by telegraph, but a new cowardice had been upon him.
This conflict extends symbolically to his ability to perform his duty as Marshall. When we meet Wilson, we are told by the townspeople's conversation how much they trust and rely upon the Marshall to keep them safe through his unquestionable courage and integrity. The implied extension of the Human versus Self conflict is the question of whether the Marshall will wane in courage now that he has a bride to protect. This is the significance of the conflict with Wilson. While Potter's bride is standing at his side, without a gun on his person, the Marshall stands up to Wilson's drunken rage without a quiver or a hesitation.
Now his conflict against himself is wholly resolved: (1) he knows the town will accept his secret marriage because he and his bride have both survived the crucible of fire (Wilson's gun-waving challenge) and (2) Potter has confirmed for himself and the town that his courage and integrity have not and will not wane as he is unflinching in courageously performing his duty.
"[If] I'd thought there was going to be any galoots like you prowling around when I brought my wife home, I'd had a gun, and don't you forget it."
The main conflict of the story is character vs. society, because the young couple’s marriage is contrary to the expectations and principles of social norms.
At issue is the fact that the young couple does not feel comfortable in their society. For one thing, a marshal did not usually marry. So they already felt like outsiders and had that guilt.
Jack Potter is described as a “prominent person” who is “feared in his corner.” He is losing some of his status by marrying.
He ….had gone to San Antonio to meet a girl he believed he loved, and there, after the usual prayers, had actually induced her to marry him, without consulting Yellow Sky for any part of the transaction.
To make matters worse, his new wife is neither young nor pretty. Neither seems to have much confidence on the journey. They are both worried about what society thinks of them, especially what the people of the town will think.
Ironically, the marriage that causes so much trouble also saves Jack. When he has an altercation with “Scratchy” that threatens to turn to a shoot-out, the marshal tells the outlaw that he has no gun because he is married. Scratchy is so baffled that he just calls the whole thing off and leaves, not knowing what to do.