In "The Interlopers," what caused the men's relationship to change?

The change in the men's relationship is primarily due to Ulrich's generous overtures to his archenemy, Georg.
After being pinned down by the beech tree, the men remain stubborn, despite their helplessness. They exchange insults and speak angrily to each other. Both know that help may not arrive for a while and that the situation is dire. However, neither will relent.
Eventually, Ulrich manages to grab a hold of his wine flask from one of his coat pockets. He wearily draws it to his lips and takes a drink. The warming liquid gives him a measure of comfort. As he looks over at the injured Georg, Ulrich begins to feel a twinge of pity for his old enemy. On a whim, he decides to offer Georg a drink from his flask.
For his part, Georg rejects Ulrich's kind offer by saying that he never drinks with an enemy. By this time, both men are in great pain and are severely weakened in strength. Ulrich then tries a second time to make peace with Georg. He speaks kindly and with great conviction:

“Neighbor,” he said presently, “do as you please if your men come first. It was a fair compact. But as for me, I’ve changed my mind. If my men are the first to come you shall be the first to be helped, as though you were my guest. We have quarreled like devils all our lives over this stupid strip of forest, where the trees can’t even stand upright in a breath of wind. Lying here tonight thinking I’ve come to think we’ve been rather fools; there are better things in life than getting the better of a boundary dispute. Neighbor, if you will help me to bury the old quarrel I—I will ask you to be my friend.”

It is a long time before Georg answers, but when he does, he accepts Ulrich's offer of friendship. The change in the men's relationship is primarily facilitated by Ulrich's generous overtures to his archenemy, Georg.

Georg and Ulrich hate each other so much that on the night the story takes place, they are actively hunting each other. But an interesting thing occurs when they meet face to face: They hesitate. Neither man is prepared to take another man's life. In spite of their mutual hate, something prevents them from resorting to murder:

But a man who has been brought up under the code of a restraining civilization cannot easily nerve himself to shoot down his neighbor in cold blood and without a word spoken, except for an offense against his hearth and honor.

After this mutual hesitation, nature takes over and pins the men beneath the tree. They are still teeming with contempt for one another. But that previous hesitation showed that they are capable of civilized behavior.
Ulrich and Georg had always been hunters. But being pinned beneath the tree, they are vulnerable. In this helpless situation, they are now more like prey than predators or hunters. It is a terrifying experience and they only have each other in this case. Faced with the potential of not being rescued, Ulrich makes the first gesture. Eventually, Georg accepts his friendship. Facing a life or death situation (together) is what really puts things into perspective and brings the men together.