According to the ever useful Urban Dictionary, the black card is defined as "an imaginary card that all black people are born with and that mixed people have to earn; that is constantly under threat of being revoked if said black person does not act black enough or in proper black ways." Now, I know this sounds ridiculous but trust me, it's real. Some people believe that they have the right to tell people if they are or are not black enough to be a "real black person."
If you are of African descent where your roots, no matter how far back, go to Africa, then you share the same history as other black people. No matter the level of melanin in your skin, you can identify as a black person, and no one should have the power to take that away from you.
Some people use the way you speak as a means to judge you. I went to get advice from an administrative worker recently, and because I was being polite to him since he was an authority figure, I spoke to him using standard English. He proceeded to inform me that I sounded like a white person and that it is "terrible" because I am a black girl. I was appalled because my black identity was called into question just because of the way I spoke.
I know somebody who went to a predominantly Asian high school, and because she liked Japanese anime and Asian cuisine, people wanted to take away her black card because she wasn't into things that black people were into. First of all, it is stereotypical to think that all black people are interested in the same things. Second of all, black culture is amazing and very important, but not participating in some aspects of black culture does not take away your black identity.
You can't quiz a black person, and then, if they are not aware of certain facts of black history, revoke their black card. Some people are socialized differently. Some people are not in an environment where they would learn these things. Instead of putting our fellow black people down, if you meet someone that is not conscious of black history, then use the opportunity to educate them and spread awareness.
Blackness should not be something that needs to be earned. If you are black, then you are black. If you aren't black, then you aren't black. It's that simple. It is not society's place to decide, judge or place stereotypes anyone.