How can literature help us approach social justice issues?

To understand literary fiction, a reader must understand the different thought processes of varied characters. Tragedies are impossible to grasp unless one understands the conflicting desires that lead characters into conflict and inevitable doom. Romances seem passionless if one cannot see what the lovers see in each other. Dramatic irony is meaningless to someone who cannot track what individual characters do and don't know.
This ability to put oneself in characters' shoes is a skill that can be trained with practice. It's also a skill that applies to day-to-day life. In that context, we call it "empathy. Empirical evidence has borne out the theory that reading literature improves empathy. And empathy is essential for fighting society's many ills.
For example, many people have accused football players like Colin Kaepernick of protesting America or its national anthem. But the truth is, Kaepernick is actually protesting numerous instances of black men being shot by police without consequence. If you personally feel that his protests are disrespectful or inappropriate, that's your prerogative--but those who misapprehend his point completely are not meaningfully contributing to a solution. Convincing his supporters to change their opinion requires one to start by understanding what they're protesting, what they know and don't know, and what they believe.
Nate Boyer, an NFL player and former Green Beret, understood this. He was very upset by Kaepernick's decision to sit for the National Anthem. So he and Kaepernick talked. Kaepernick didn't necessarily value the anthem the way Boyer did, but he understood that it was important to Boyer. Likewise, Boyer didn't agree with using the anthem as a form of protest, but he understood why Kaepernick felt that it was vitally important to make his cause known. This comprehension of other viewpoints--the same skill that students learn about in literature class--led to a compromise, in which Kaepernick agreed to take a respectful knee, like a soldier at a colleague's grave, rather than simply remaining sitting.
https://www.snopes.com/fact-check/veteran-kaepernick-take-a-knee-anthem/