It may not have been oppression because of race, but it was still oppression that was dealt with by one single race.
Fighting for survival on through 1812? Good thing you stopped there, because if you'd gone to conclusion of the War of 1812, in 1814, you might have had to deal with the issue of an extremely diverse American force defending New Orleans. The commander was Andrew Jackson, and he used an assortment of slaves, Indians, and white volunteers, as well as Caribbean pirates, to defend the city against the British.
That's all trivia though. It would have to be oppression because of race to unite us all together as having "white culture." Instead it was oppression because of nationality, which is part of the reason we have "American culture" today.
And anyway, when I'm talking about oppression I'm talking about the really hardcore, down and dirty oppression, like what happened to slaves in the American south. All vestiges of previous cultural identities were more or less wiped out by that experience, so they formed a new culture - together, not identifying as Mende tribesman or Nigerian nationals, but as blacks. Being black was the only thing, besides their servitude, that brought them all together. The same is not true of American revolutionaries - they had that new sense of nationality to unite them.