Southeastern Native American groups often, though not always, readily accepted non-pure natives into their families. "Acceptance" in this part of the U.S. was basically a native issue, because whites in the southeast that took on native women were typically individualistic, agrarian/plantation types that were usually separated from the emerging white-populated cities.

In fact, many of the leaders of the Cherokee in the early 1800s (and since), were mainly whites, with some native blood, of course, that had merged into Cherokee families. Their children, naturally, were reared in the Cherokee fashion.

Fundamentally, most southeastern natives identified themselves racially by their mothers.

Further reading on this topic: Cherokee Women by Theda Purdue; also Creeks and Southerners: Biculturalism on the Early American Frontier by Andrew Frank.