"People are showing up at our door and we've finally learned to welcome them.
This is a Good Thing indeed!"
Well, we still feel bad for them that they're not Greek, but we don't tell them that! :)
Guess we're a step ahead of you then, because whatever "ethnicity" (is this a code word for "race"?) they are, they can always become Anglican. And we actually have quite a mix in our church, far more than any of the Episcopal churches I grew up in: not mentioning the (born) Brits, Americans and Canadians in our midst, we also count a number of Asians and Indians (both kinds, native and otherwise) amongst our midst.
But then again, "ethnicity" in Anglicanism disappeared a long time ago. I remember being told as a boy in Confirmation Class that the "average Anglican" (I quote exactly; as an engineer I might dispute the adjective) was a poor black African woman.
But if the New World Orthodox can "lose" the "ethnicity," I see a big future for you all -- having observed converts who've gone over despite the negatives.