It's another way of creating in groups and out groups, who is cool and who is not. Someone is not cool if they are not reflecting perceived essential qualities that make someone fit in with the group or culture they are accusing them of not being faithful to. It's almost seen as a kind of disloyalty or betrayal of the race. It makes people affirmed in the idea that there is some essence or core of a person which identifies them as the label they are supposed to be and if they don't follow the script or behavior patterns stereotypically associated with that group, then they are not "black enough."
In our world, we like labels and categories, and definitions. They make us feel we know who or what it is we are dealing with. It makes us uncomfortable when people don't fit into neat categories, so we describe them as being opposite as
@ruji mentioned, or as negative examples of what it is when someone is not being what they "should" be. It's also tied to a false sense of what it means to be "real". We have these forced ideas about what makes someone real.
For example, I've been told I've lost my culture or that I'm hiding it because my accent is not longer as strong. So, I'm no longer a real . . . . because I'm not obviously and visibly reflecting the behavior of someone who is authentically living in that place anymore. The assumption is I'm not longer as real, because I'm not speaking the dialect everyday and not singing the songs or participating in the culture regularly, despite still feeling every bit of my home culture in me, as a person, memory, experiences, consciousness. Now I'm seen as less of this culture, even if I don't feel this way. But honestly, I am likely more American than my home culture at this point in terms of behavior, but I think of myself as a mix of both cultures. Why do I have to choose? Labels. We don't give people the right to choose. We make them choose a side, and then scold them for not choosing the "right" side.
I've also been told I'm not as loud as I was expected to be. Naively, I thought this was a compliment at one point, not realizing how insulting it was to believe this. This comment implied some belief that speaking loudly was some indication that a particular group didn't know how to speak appropriately and quietly, indicating they were less sophisticated as communicators, and didn't know better (which supposedly meant less educated). Speaking evenly and with a moderate tone was considered a sign of status and "good breeding"

in previous centuries. At some point, it was determined that speaking quietly, and calmly is associated with decorum, composure (aristocracy), and superior upbringing. That's what proper ladies and gents do. So, clearly, those who spoke loudly didn't have the right breeding, and didn't know better.
As ridiculous as these ideas sound today, these are the assumptions which guided much of our thinking for a long time. Ironically, speaking loudly was also associated with speaking out of term, essentially challenging the authority, and questioning the status quo. No one likes anyone challenges the status quo. This is why the Uncle Tom persona was seen as good and bad. He was submissive, which was seen as supporting the justification of slavery. If the slave would just behave and act properly (similar to the way the master's behaved or the way the master's expected them to be behave), then they would have it easier, be rewarded, treated better, able to be redeemed from the inherent evil of being black, etc.
The Uncle Tom was considered a huge problem of course because it supported the view of the slave as someone who could be redeemed of their "black" nature by doing things to please the masters, adopting traits of their masters, showing they were capable of good and right qualities. It meant they could overcome the inherent "badness" that came with being black if they were to behave the right way. Being accommodating and submissive was perceived as catering to the belief that being black was inherently wrong, but could be redeemed with good behavior.
On the other hand, any slave or freeman working with the masters would be seen as compromising if they behaved as they did. They were seen as race traitors, unfairly so. Many went along to get along, and that was seen as betrayal, although it may have saved many their lives.
The tendency for a long time was to support stereotypes of blacks as mostly loud, boisterous, reactive, and angry. This mean that they were being abnormal or Uncle Tom-like if they are calm, relaxed, thoughtful, and even tempered. Clearly, that's not being a "real" black. *rolls eyes* So, there you have it. The history of the perception of blackness in a nutshell.
Stating that someone is not _____ enough is also part of the idea that people should reflect their race, a social construct, in how they think and behave. It's like a social contract. There is an assumption of an unwritten code book out which supposedly says everyone who belongs to a particular race believes that, "We all agree to think, feel, behave, and act in a manner commonly associated with being ____".
We have this idea that people should be defined almost entirely by their race, ethnicity, or nationality (and gender). These things are seen as key features of who someone is and the main way people come to learn about and understand each other. Without these categories, we feel lost, and are not sure how to interact, so it's easier to have these specific things we can identify as a set of traits to make us feel affirmed in our belief that people have a core self that can't be changed, though these traits are purely arbitrary, made up social categories and descriptions.