Kamehameha Schools, also known as the Bishop Trust, does NOT let anyone in that cannot show Polynesian-Hawaiian ancestry. So, NO they don't have a preference.  They only allow one race as they see it in "their" schools. That is why every time they are sued they have settled out of court.  
They are clearly in violation of Supreme Court rulings pertaining to school segregation.
The last kid received an out of Court settlement of $8 million dollars.  Because of the death threats he and his family received they had to move to the mainland for their safety.