It's not about paying for the sins of your ancestors. There's no exemption for immigrants whose ancestors had nothing to do with past harms to the native American population.
It's about helping people and a culture that is unfairly downtrodden. You may believe that they aren't currently affected by direct racism, and I hope you're right (I doubt it). But, there is no denying that they are one or two generations removed from brutal racism, and not too many generations removed from genocide.
You can't take everything away from a group of people and then expect them to recover in a generation or two. Even without residual racism, that is unrealistic.
You can argue that you don't want to rely on the government to decide who needs help, but if you travel around and see what it's like in the places where the government doesn't play a role in helping the downtrodden, I don't think you'd want that for your country.