I've played a bit into both the Imperial and Stormcloak questline using alternative saved games. What happens if you choose not to join either faction? Does the main quest require a choice? I see my character as a bringer of change. A unifier rather than a divider.

The Empire would hail him a hero because he slays dragons and Stormcloaks aside, I would think that the Empire would view the dragons as the greatest threat in the region. Also, I would think that any Imperial not really satisfied with the conditions of the accord between the Aldmeri Dominion and the Empire, be they Nord or otherwise, would long to see the old days made anew with a new Dragonborn Emperor (though they would never say so openly for fear of persecution from the Thalmor and the Legion

The Nords would hail him a hero because he slays dragons, and Imperial soldiers aside I would think they would view the dragons as the greatest threat to their homeland. Being Dragonborn as Talos was, they would see him as the single greatest hope for a return to the freedoms of old before the Empire banned the worship of Talos.

My character would view himself as neutral. His true enemy being the Alduin and the Dragons. When that threat is dealt with, what future might he have?

What happens if I choose neither the Imperial Legion nor the Stormcloaks? Does the game allow for both to be united behind Dovahkiin?

Because when I join either faction, I feel like I'm on the wrong side. Does that make sense?

You don't have to join them. it is entirely optional.

They come to a temporary peace untill you kill the dragons the proceed to kill each other.

Neither side care about the dragons, they almost tell you to gtfo when you try to make peace, but then the blades tell them to s t f u