A public school should be open to anyone in that district, and in some cases those outside the district as well. Opening schools up to one race would only be a step back into the past. Although it may seem beneficial to open a public school only to a minority race, it would not be beneficial in the long run.
No, public schools shouldn't be limited to one minority. Before segregation that was the norm, and it equaled to inequality educationally and economically. There can be a predominate assumption that a particular race is in abundance at a school, but never limiting to one race. Private schools already assume that position, of being more selective.