This is a difficult question answer but I will try to help. I'm a NON-WHITE person. I'm of 100% central american and I see a huge difference in culture between me and a white person. My culture is vastly different than white peoples in that my culture celebrates and encourages passion and emotion. My culture teaches us to be very expressive in our facial gestures and we are normally very animated and energetic. We thrive on the company of friends and family and we are taught to be grateful for everything we have. We sing, dance, cry, laugh, get angry, and sad all at once because we only know how to release our emotions. We are very hospitable where we make sure that our company feels like family and we are quick to offer help and food. My culture is free-spirited, loud, and kind.
Generally speaking, I see white people as very reserved, organized, tranquil and sometimes boring. This is not a bad thing. But I can see how a NON-white person can tell a white person to "stop acting so white". They probably mean "stop acting so uptight and relax". This is because white people tend to be very quiet and collected and they seem to care a lot about what people think of them.
I'm speaking generally of course and not all WHITE people are the same and not all NON-white people are the same. This is just my interpretation.