Setting is a very important part of many stories. As the question suggests, setting can influence a character's actions, feelings, and/or decisions. For example, the lone survivor motif is a popular genre. Stories like Hatchet, "To Build a Fire," "The Most Dangerous Game," and even The Hunger Games feature main characters that are thrown into a setting and situation that requires him/her to fight for his/her life. Without Ship-Trap Island, Rainsford never has to question the validity of hunting humans. Without the frozen Yukon, making a fire isn't such a lifesaving necessity. The time period of a setting is equally important for determining how a character will act. Take Isabel from Chains. She is a young black girl living in New York during the time when slavery existed. The author, Anderson, is forced to make Isabel behave a certain way because of the existing setting for this story.
This particular eNotes question is linked with the story "Two Kinds," so I assume that the question is asking about this particular story as well. The opening lines of the story give a great indicator of how setting can powerfully influence the thoughts and actions of characters.
My mother believed you could be anything you wanted to be in America. You could open a restaurant. You could work for the government and get good retirement. You could buy a house with almost no money down. You could become rich. You could become instantly famous.
Jing-mei and her mother live in America, and Jing-mei's mother is heavily influenced by the stereotypical American Dream. She believes that a rags-to-riches story is possible, and she believes that working hard toward that goal is the main ingredient toward achieving that dream. Because she believes that a person can choose any path, she chooses for her daughter. Jing-mei's mother chooses each thing that could make her daughter rich and famous. In her home country, this wouldn't be an option, so Suyuan wouldn't have behaved in this way. However, being in America allows her to push her daughter into a life that isn't subservient to anyone. Unfortunately for Suyuan, the American setting also works against her. Jing-mei is growing up in America, and she gets to see people choose their own destinies and passions. Jing-mei realizes that she doesn't have to be who her mom wants her to be. Jing-mei can choose her own path and have her own dreams, and this is a reality based on the story being placed in America.
I looked at my reflection, blinking so that I could see more clearly. The girl staring back at me was angry, powerful. She and I were the same. I had new thoughts, willful thoughts—or rather, thoughts filled with lots of won'ts. I won't let her change me, I promised myself. I won't be what I'm not.