But on the other hand, I believe the Jarl of Whiterun says that Whiterun is on "Whiterun's side", suggesting neutrality, though I could be wrong on this point. There is also an unmolested Talos worshipper in Whiterun, in defiance of Imperial law.
From a RP perspective, as a Thane of Whiterun, the Dragonborn should be sworn to the service of the Jarl, though I believe no oath is ever sworn. Nonetheless, the Dragonborn should choose the same side in the war as the Jarl or else be an oathbreaker. However if Whiterun is truly neutral, the Dragonborn would probably have some leeway in choosing one side or the other. I would have preferred a choice to accept or refuse to Jarl's offer of a title to prevent the Dragonborn being bound to his service.
Any thoughts? Especially with regards to the other cities.

for the legion!