I live in Southern Colorado, where there are many bi-racial people. Many of them are 1/2 Mexican and 1/2 Caucasian, but they usually drop the Caucasian part and just claim to be Mexican.
Yes, quite a sad thing I have to say. Usually people who are half-Hispanic and half-white (like George Zimmerman) are generally classified as Hispanic (same goes for half-white, half-African Americans, like Barack Obama). That's because they show their non-white side a lot more.
As for Eurasians like me, we pretty much look completely mixed. We're neither labelled Asian or white, we look very different from both. Our skin colour and facial characteristics make us look like a whole different ethnicity. People like Maggie Q, Keanu Reeves, Kristin Kreuk...it's hard to categorise them as either white or Asian.
I'm very much white, however my heritage is half Ashkenazic Jewish (who were treated as a separate race in Europe for centuries.)
Interesting, I'd be very proud to be part Jewish. I have Middle Eastern links, my Italian family resided in Sicily. We were an Islamic emirate under the Fatimid Caliphate for years, I wouldn't be surprised if I had some Arab blood. Perhaps I might also have Jewish blood as well...
I go to a Church that is 100% white. We had a mexican woman and her children here for years and years, but she moved. We also have a Lebanese family, but last time I checked, "white" included people of Middle Eastern descent. As an Orthodox Christian, my Church is about 1/2 Eastern European American (like me!) and 1/2 Irish American (Father and his huge family.)
The ethnic makeup of my Church has never been a big deal. It is what it is, I suppose.
I suppose Middle Eastern people (Jews, Arabs) are white, in the sense that they are Caucasian. They have the same skull shapes and similar genetics, but due to the climate, they're dark skinned (much like Italians and Greeks). As far as I know, Arabs are more similar to white people than Turks. This is because Turks are originally Mongoloid, many came from Genghis Khan's army.
Of course the ethnic makeup of the Church should not matter, in fact I'd say that a multiracial Church is better. This mostly applies to the Catholic Church, the great majority of our adherents are from racially diverse areas, such as Brazil.
Unlike many wacko Protestant churches, Catholic and Orthodox have never seen race as an issue.