The representation theory of stories, where the protagonist must mirror my gender, race, or sexuality for me to find myself in the story, offers a cramped view of what fiction can do and a shallow account of how it actually works. Stories succeed not through mirroring but by revealing human patterns that cut across identity. Archetypes like Hero, Caregiver, Explorer, and Artist, and structures like Tragedy, Romance, and Quest are available to everyone. That is why a Japanese salaryman can love Star Wars despite never having been to space or met a Wookie and why an American teenager can recognize herself in a nineteenth-century Russian novel.

Tom Bogle makes this point well in a post on Facebook:

I have no issue with people wanting representation of historically marginalized people in stories. I understand that people want to “see themselves” in the story.

But it is more important to see the stories in ourselves than to see ourselves in the stories.

When we focus on the representation model, we recreate a character to be an outward representation of physical traits. Then the internal character traits of that individual become associated with the outward physical appearance of the character and we pigeonhole ourselves into thinking that we are supposed to relate only to the character that looks like us. Movies and TV shows have adopted the Homer Simpson model of the aloof, detached, and even imbecilic father, and I, as a middle-aged cis het white guy with seven kids could easily fall into the trap of thinking that is the only character to whom I can relate. It also forces us to change the stories and their underlying imagery in order to fit our own narrative preferences, which sort of undermines the purpose for retelling an old story in the first place.

The archetypal model, however, shifts our way of thinking. Instead of needing to adapt the story of Little Red-Cap (Red Riding Hood) to my own social and cultural norms so that I can see myself in the story, I am tasked with seeing the story play out in myself. How am I Riding Hood? How am I the Wolf? How does the grandmother figure appear in me from time to time? Who has been the Woodsman in my life? How have I been the Woodsman to myself or others? Even the themes of the story must be applied to my patterns of behavior or belief systems, not simply the characters. This model also enables us to retain the integrity of the versions of these stories that have withstood the test of time.

So if your goal is actually to affect real social change through stories, I would encourage you to consider how the archetypal approach may actually be more effective at accomplishing your aims than the representational approach alone (as they are not necessarily in conflict with one another).