Slavery, discriminatory immigration acts, segregation, Japanese-American internment...there are many times when the United States failed to live up to the ideals of democracy and equality, and our treatment of Native Americans is certainly one of the largest examples of this. It's not talked about as much as others, but there's valuable lessons to be learned from it.
The words of many Founding Fathers stood at odds with their actions. However, those words expressed ideals which, because they were imperfectly realized, have been championed for by all kinds of Americans(including Native Americans) throughout our shared history. The Founding Fathers were very radical for the 1770s, yet they were also products of that time, and the contradictions this created continue to deeply affect our society today, over two centuries later.
I hope that one day those ideals will be realized, although I doubt I'll live to see it(and I was born this century, what can I say, I'm a pessimist).
