Yanina asked: "What do you think about the Beachy Amish?" and "I was recently in the Beachy Amish website and saw a picture of an African American girl on it. How do the Old Order feel about people of different races and ethnicities?"
Yanina, I'm sorry it's taken me this long to answer your questions. About Beachy Amish: I don't have very many experiences with Beachy Amish, (most often referred to as Beachy Amish Mennonites), and therefore I don't have strong feelings about them, one way or another. However, I will share the experiences I do have, which happened when I was in about the third grade in Amish school.
Meadow Glow School, near Burton, Ohio was still fairly new when there were several families in our church district who converted to the Beachy church in the area. The first family to convert still continued to send their children to our school. My father was adamantly opposed to the "Beachys" as he called them and didn't like us to go to the same school as they attended, as if their "Beachiness" would somehow rub off on us. I remember wondering what the big deal was -- as far as I could tell, the only difference in these daughters was their different style clothing. Fairly soon, there were other families who followed into the Beachy church, which seemed to make the Old Order Amish leaders (and others like my father) even more strict in the Ordnung of the Old Order church.
I'm finding that the Amish in Geauga County tend to be much stricter about the meidung (the shunning of former members) than many other Amish communities, including Holmes County. Many Amish churches will lift the meidung after a year, or after they find out that the person who left has become a member in a different church. They also see the Mennonite and Beachy members as fellow Anabaptists, not so different from themselves. Not so with the Amish in Geauga County. It doesn't matter whether the person leaving becomes part of a Mennonite, Lutheran, Evangelistic, or Catholic Church, or even if the person becomes an atheist, the meidung is applied the same way -- at least in most families and church districts. At least when I was growing up, the Amish saw the Beachy church as a threat, because they kept converting more Amish. They shunned the people converting to the Beachy church as a way of deterring more conversions.
I think the biggest difference between the Amish and the Beachy Amish Mennonites is that the Amish rely on retaining their young to maintain their communities, while the Beachy Amish Mennonites rely more on converting new members to propagate their congregations. Which brings us to your second question.
Because the Amish rely on retaining their young to ensure the survival of their religion and way of life, they have not had to confront issues of race and ethnicity. For the most part they see themselves as separate from not only "English" people, but anyone else who isn't Amish. Though, your question raises an interesting issue: Would they allow someone of color to join? They will occasionally accept someone willing to join their religion and way of life to become members of their faith. Just as the Amish have separate beliefs from the outside world in matters of religion, my guess is, if pressed, their values on this issue would also be different than the outside world -- in other words they may not share our value of being all-inclusive, especially in matters that would concern their culture. One of the things that holds their culture together is shared experiences and shared ancestry. This makes it hard for anyone from the outside to join the Amish from both the Amish point of view, and that of the person joining. My guess is that the Amish resistance to someone of color joining the church would make it uncomfortable enough for the person thinking of joining that it probably wouldn't happen. At least I never saw anyone of color among the Amish.
As for the question of how Amish feel about people of other races and cultures in general, I would say they probably don't have enough exposure to have strong feelings one way or another.
It does not surprise me that you found a picture of an African American girl on a Beachy Amish website because they believe in going out and saving as many people as they can. They are open to all races and ethnicities receiving their essential message -- that Jesus Christ as one's personal Lord and Savior. They believe that one must hold this as one's central tenet, otherwise salvation cannot be achieved. In fact, those who are born-again Christian, whether they are Beachy, Mennonite, or from any other denomination, see it as their mission that everyone in the world find out about the gospel. Most often coupled with this belief is the one that because God created everyone, it applies to all, no matter what race, ethnicity, or culture they are from.
Thank you for your questions, Yanina.