Skyrim has been a part of the Empire hundreds of years, so I'd assume it does.
So was the USA part of England or most of South America part of Spain (My own country, BTW).
Empire only executes Talos worshippers because of the Thalmor are demanding it with White-Gold Concordant. What comes to the second point; feodalism simply isn't racism, it's not based on race.
And It might just as bad. The Empire is reduced to three provinces, whithout Skyrim probably just Cyrodiil, and Its rulers are no longer their rightful founders, the Septims. Besides, Hammerfell did fine without the Empire against the Thalmor, It's in the lore.
@Scow: It's not racism, though, It's intolerance or Xenophobia.
@Pistolero: All human pertain to the same race, the Homo Sapiens Sapiens, part of the Homo Sapiens species. There are several ethnicities or ethnic groups, though. In Tamriel elves could be considered part of the same species as men, for they have fertile offspring when they breed, though they're probably a diferent race.
Me? I think every nation has the right of self determination, and such thing is only achieved by brute force (not anymore, though, for different reasons). The Empire might want to rule over some provinces, but has no right to do so, and needs to make full use of Its strenght to keep It that way.