So do you have to take a side (Empire or Stormcloak), or is it possible to get them to come together as a single force and take the fight to the Thalmor to free Skyrim once and for all?

Or is the civil war really that black and white?

Well, the two sides are not black and white, but you will have to choose. The disagreement between the two sides is irreconciliable.

And not getting involved leads to the Thalmor winning in the long run.

You are the synthesis of the Blades' and Graybeards' stances on world affairs.