It depends on who's talking. Sometimes it can be good things, such as using proper grammar, being polite, and avoiding crude humor. Sometimes it can be bad things, such as being racist and judgemental. It can mean being white trash or redneck, or Posh and Ivy League. There is no true "acting white".
There was an issue lately where police were accused of being racist because they docorated a tree with wrappers from things like takis, funions, cheap beer, KFC, and cigarettes. These are things that are supposedly associated with blacks. Confused the hell outta me because my white redneck relatives love all that stuff. (I would say those things are associated with being poor though).
(Also in my area, most black families won't touch KFC. It's Churches Chicken all the way. And yes, that comment might be a touch racist)