The Native Americans did not "lose a war" and they were not assimilated. They were forcibly removed to reservations on the poorest, most barren land in America (where many continue to live to this day). The America that did this WAS white and American continued to be ruled by whites until at least the 1960's civil rights movement. For example, the army was still segregated in World War 2. I believe every officer and 99.99% of all soldiers who participated in the ethnic cleansing of Native Americans were white, supported by an entirely white government, paid for entirely by the taxes on white businesses. White, white, white. So just try to whitewash that.
How was the Trail of Tears a "war"? How is that assimilation?
The Cherokee were white? They were Jews? LOL. Wow. OK, we can add anti-Semitic to the list of American sins.