Thanksgiving in the U.S.A. has become a season not only of Thanksgiving, but also (unfortunately) a season of collective shame and regret over what our forefathers did to the Native Americans. I'd encourage Christians to take the lead in being clear-headed and constructive on this front, not by sweeping the shame and regret under the rug, but by acting with deliberate generosity towards the Native Nations.
Do we share the blame for the wrongs committed by our ancestors? I'd expect we only share in the blame if we see the continuing injustice and take no action. The Native Americans welcomed us; they did not begin by thinking we should go back to Europe or that we should have nowhere to live in the land. But they did seem to think they would be treated with justice and treated as friends, and they did seem to think they would have a better outcome than we have since given them.
Many churches already have outreaches and ministries to the Native Americans, but despite that extreme poverty is still rampant. I'd encourage you to consider beginning your Christmas shopping at a Native American-owned shop. If you don't know one near you, several links are available below. Cool jewelry? Check. Nifty pottery? Check. Beautiful weavings? Check.
Southwest Indian Foundation
Eagle Dancer Gallery