I'm taking into account that the original poster of thread had trouble titling it , but I must say I really find the title offensive.
What is a non-ethnic role?
As far as I can see everyone has an ethnicity. Just as everyone has a speaking accent.
I know living in euro-centered world this is hard for some white people to understand, but white people aren't the "pure" example of what it means to look like a human.
So judging by the title of this thread:
non-ethnic = white
ethnic = anything other than white.
How sad it is that the vast majority of the human being on this planet are considered "ethnic" while a small minority are the "norm".
As for the subject at hand:
Drama is about conflict, should the conflict be racially based then casting race specific actors is called for.
Example: It would undermine the conflict of GONE WITH THE WIND by casting a black Scarlet O'Hara.
But you could easily cast a black girl in the role of Annie in ANNIE because the conflict that keeps the drama going in the world of that play has nothing to with race.
That said, you have to take into account the audience imagination or lack thereof.
One of the remarkable things about Audra McDonald is her talent is such that audience doesn't see a black women playing a white role, they see the character.
Great minds discuss ideas; average minds discuss events; small minds discuss people. - Eleanor Roosevelt