Whiteness is the norm, but is there white culture? Only, I think, to the extent that we want BIPOC act like us, so that we can feel comfortable; so that we are not required to listen, learn, and risk change. Because it seems that the only reward for acting "more like whites" is being told you are articulate, or you are one of the "good" ones.
Perhaps the biggest irony is how many white people like to take on the black or hispanic culture because it's cool, yet we discriminate against the the people of those cultures. And if that isn't the most glaring example of privilege there is, I don't know what is, except perhaps for responding all lives matter to Black Lives Matter protestors.
White people get defensive easily when privilege is brought up. using the "I worked for everything I have" line of defense. And they very well may have, BUT they didn't have to work harder because they were white. I think a lot of white people get hung up on that word privilege. It doesn't mean wealth; it just means that no matter how tough things were, your skin color didn't add to your problems.