I'm not sure any hard and fast rule can work but typically in my view:
1. If you have a Black parent or grandparent I can give you the benefit of the doubt. If only one Black grandparent, their biracial parent may identify as Black like most older biracials (pre-millenials) do. With one grandparent though how and where you are raised is pretty influential in self-identification. Many pass. I know many people howl about "this person is only 25% Black" but if someone can pass and doesn't (i.e. Adam Clayton Powell) I see that as a point in their favor and am not going to be tripping.
If someone mixed doesn't want to be Black though, they can do their thing. I am not in the game of forcing anybody who doesn't want to be associated with us.
2. If they are light but have a continued line of family members who considered themselves Black (light skinned/creole families) then they essentially came from a Black family though they may look mixed or supposedly "not Black enough". In this case their Black percentage means less to me than the fact they came from a line of family members who though they have been light skinned, identified with the Black community. Valerie Jarrett's family is an example.
Outside of this with people claiming a Black great-grandparent or something but their parents and grandparents consider themselves White, I am usually kinda like
Not because I believe in racial purity (the above should make this clear) but I have to wonder about someone claiming a sliver of Black ancestry when no one in between did. Maybe the only exception is people like Melungeons, or someone else, who tried to hide and suppress their Black heritage but were outted by genetic science. In that case maybe they can rediscover their heritage.