Say a white man had an affair with a black woman in pre-civil rights, post slavery America, and left her to raise the child herself. How could we expect that child to be thought of and treated as they grew up?
They would be treated as African American under Jim Crow laws. See the "one-drop rule", that basically stated that any amount sub-Saharan African ancestry made that person to be considered black, socially and legally. There was no 'halfway' on racial classifications at the time.
That child would for all practical purposes have the same experience as an illegitimate, 100% African American child in that place and time.