I’m not sure I know what ‘white culture’ is. I've seen the phrase "acting white" in modern discourse. It usually seems to reference acts of literacy, numerancy, and\or articulation. Not sure if that's related or not.
Acting white is a racial stereotype. Not every white person holds literacy, numeracy, and articulation in high regard or even practices it. There are plenty of white dopers who in their 30s are still living in their parents basements, and plenty of white people who embrace thug culture. You can see them on episodes of “cops” and on Jerry Springer all the time.
I say the we should abolish the phrase “acting white” due to it's racist overtone and substitute it with the phrase “acting successful”.