Culture, reasonably understood, isn't tied to skin color generally. American blacks are an exception, which I'll get to in a second. Culture is generally understood to be a product of shared morals/virtues/aesthetics/etc that happen in geographical proximity. Culture is tied to where we are, not what color we are, generally. Black british citizens are culturally british. White Brazilians are culturally Brazillian, as are brown Brazillians, and black Brazillians.
So it's not white culture, but rather European, or American culture.
Now to my earlier exception. American blacks are an exception because they were lifted, en masse, from their homes and transplanted into America, where their native cultures were systematically squashed. People without traditions and cultures invent them, and borrow from others nearby. Americans themselves are mostly transplanted, and in some case jettisoned their native cultures for political or social reasons and attempted to start over. So we wound up with a bunch of Europeans who had rejected their native culture, trying to impress a new culture on a bunch of black people from different locations, while simultaneously forcing them to jettison THEIR culture.
So black slaves melded multiple African cultures and the variety of European cultures in ad hoc ways to create anew culture and identity, because they weren't given any other choice. Since the number of historical slave transplants of this magnitude are fairly small, the birth of this new culture was unusual, both in its speed of spread and its creativity. With traditions stripped away, artistic black people had a clear field in which to create anew, and they did.
And since culture is proximity driven, that new culture became part of mainstream American culture, too. Slave owners forced Christianity on black slaves, who responded by creating gospels, which were picked up by European descended Americans and fed right back into the burgeoning American culture. They gave recently freed but still uneducated black musicians European notation and symphonic instruments, and in return blacks created Jazz, which Was absorbed into American culture.
And it's not just blacks in America, but virtually all of the immigrants. Jews gave us comic books, movies, and vaudeville, which led to stand-up comedy, another American art form. Virtually all the American art forms came from the melding of our immigrant and/or slave cultures.
So, my answer to the OP is that you've misunderstood the nature of culture, and consequently asked a question that doesn't make any sense. While groups can try to carve out their own pocket, or sub-cultures, inevitably the syncretic American culture is voracious and will adopt them all. It's not because white peope are bad and mean, or even because they really intend to, it's because culture spreads with contact. If you want to keep a sub-culture to yourself, as any hipster knows, you can't share it with people.