Honestly it is a lot like this in Skyrim already, Nords and, to a lesser extent, Imperials are the only races that really make sense for the main character. Altmer, Bosmer and Khajiit all have close ties to the Thalmor, which you can't join. Redguards feel deeply betrayed by the empire and might fit in with Stormcloaks if they weren't so xenophobic. Dunmer, being elves, wouldn't be regarded in any esteem by the nords. Argonians... are cold blooded?
Nords make the most sense, but all races live in Skyrim, with the exception of possible Khajiit everybody could have a reason for joining any particulair faction. Though it's definitely true that most would be more inclined to join the Empire instead of the Stormcloacks there is something to be said for people joining both factions, even when joining the Rebels there is no real hatred for somebody who isn't a Nord, you're just frowned upon. The same applied to Morrowind, you weren't a native so you weren't as important. None of the great houses loved you at first, and the ashlander tribes were certainly cautious of a foreign Nerevarine... Still everybody could have a very good reason for wanting to join one side or another, I see no real problem there.
In Summerset it would be different however, the Isles have from what I can gather pretty much kicked out all non Thalmor and place a heavy preference on Altmer where Bosmer are second, Khajiit are probably allowed but then regarded as third rate citizens and the rest can kiss their ass. There would be no logical way for an Imperial, Nord, Dunmmer, Redguard, Breton, etc. to walk around there and be anything important or you know walk around there and not be hunted down on first sight by some Thalmor agent.
None of that matters, because we aren't playing a *race*, we're playing an INDIVIDUAL whose inclinations and actions are entirely his own, and not rigidly determined by the parents he was born to.
True in Skyrim, not true in a place where every none Dominion race would preferably be killed on sight by the very government... There is no way you could start out as a small time ex-convict in a place like that.