I’ll bite. Bear in mind that this is used as a criticism, and sin is usually in the eye of the beholder.
“Too white” means that the person who is being criticized is acting in a way that is, at best, more like white culture than the culture of the ethnicity they belong too. At worst, they’re throwing their fellows under the bus to get brownie points from the people in power.
Michael Jackson was accused in his time of being an oreo because the plastic surgery he had to make his face look more caucasian. Unfair, IMO, because he was raised in an environment that said that was the only acceptable way to look. That’s the only specific use of the term “oreo” I can remember, but I have heard it in referring to others in the past, just can’t remember specifics.
In light of my interpretation of the terms, I’d guess that the closest common phrase would be “going native”