The thing about identifying as a member of a particular group is that people frequently only do so when it's perceived as advantageous. For example, there have been times in recent US history where passing as "white" opened up opportunities for people and allowed them to avoid danger. When a person who identifies as "black" despite a lack of recent African heritage or a family history that contains it, I sometimes have to question what kind of advantage that person attempts to gain, and whether he or she is willing or able to accept the down-side of belonging to a less privileged group.
I understand how a person adopted into a family often takes on the culture of his or her parents regardless of genetic reality. A pale child adopted by a melanin-gifted family and raised in a culture best described as "black" could be excused for checking the "black" box on a government survey. I am old enough to remember the country singer Shania Twain being accused of cultural appropriation for using an Ojibwa name and "exploiting" the Ojibwa culture, because although she had been adopted into and raised in an Ojibwa family, she was not genetically Ojibwa and therefore "not Ojibwa enough". It doesn't seem like a big stretch of the imagination to envision the same thing happening to a person raised by "black" parents. Then of course there was the whole drama with Elizabeth Warren's claim of partial First Nations ancestry, which was supported by a DNA test, but which did not reveal enough of a genetic percentage to qualify her for tribal status. Even tribal status frequently depends on whether a person is "enough" genetically to qualify: whether he or she has "enough" ancestors that come from the tribe. No matter where you draw the line, there's always someone who's on the wrong side of it through no fault of his or her own.
I've got a personal preference for inclusiveness, but that comes from an abundance mentality. What happens in an environment of scarcity, when there are only so many goodies to go around to the member of the in-group, and when including one person means saying "no" to another. One example might be a scholarship or grant available only to a member of a less-privileged group or minority. Another example might be tribal income available only to registered members of the tribe, such as the Osage "head rights" that existed during the oil boom in the early 20th century. The more people among whom the assets must be distributed, the less that is available to each individual.
For a person who wants to be "black" when there are scholarships or affirmative action opportunities to go around, I kind of have to point out that the affirmative action only exists to compensate for some pretty pervasive and ongoing inequality. So, I kind of have to ask: what steps are they taking to ensure they take the bad along with the good? How "black" do they want to be, if they happen to be driving a rental vehicle at night and take a wrong turn into a street known for drug trafficking, but accidentally make a driving mistake due to their unfamiliarity with the area? If by some chance they make a bad choice and end up in prison, how "black" do they want to be? What's their plan for interacting with people who assert that they aren't "black" enough? How important is that identity? Are they willing to embrace the negative stereotypes? Are they willing to spend time interacting with people who are making bad lifestyle decisions simply because those people happen to be part of the ethnic identity the box-checker wants to claim?