Most Americans don't have any clear conception of who the Amish are or what they believe. Those "mainstream" Americans who live near Amish settlements see them either positively, negatively or indifferently. Most "English" (what the Amish call non-Amish) simply don't know Amish people well because the Amish tend to associate mostly within their community, unless they want to buy something from the outside or sell something to the outside.
My sister-in-law lives in an area that has an growing Amish population. People there may feel slightly "under threat" as Amish families move in groups and buy up farm land. They then compete for land, livestock and certain kinds of equipment. My sister-in-law used to have a rather negative opinion of them, mainly because they seemed stand-offish. My brother-in-law seemed a little more positive toward them, but then he is generally easy going and also had more to talk about with the Amish, mainly livestock and equipment, when they met at auctions. Now my sister-in-law and her husband have taken their dairy farm organic and they have found that Amish farmers are interested in exchanging information about animal husbandry, natural pest control and so on. My sister-in-law has a much more positive opinion of the Amish now. The key, of course, is that she sees them as individuals, not representatives of a stereotyped group.
An Amish crew in Iowa did some work for my father, and he got along quite well with the crew manager. After they completed the work, they invited my parents to some event in their community. I believe my parents were the only "English" there. This kind of thing happens to my father, though, who must come across as relatively friendly and open and willing to talk to anyone. They were also the only white people at a very large African American wedding in Chicago (invited by a former student of my father).
Mennonites are a related group, but they vary widely in the extent to which they are "integrated" into mainstream American society.
I personally feel that it is unjust to criticize Amish parents for not preparing their children to live in the mainstream world, since that is precisely what Amish don't want to do, and I feel they ought to be allowed to follow their beliefs. Amish young people are given a choice of continuing to live with their community or go out into the world. And while it is certainly not easy to do, some do choose to leave. I have Mennonite friends whose relatives separated from the Amish and now live as Mennonites.
While I understand that the United States has not always been perfectly open to religious minorities, the country has still done pretty well on the whole and I am perfectly willing to have Amish, Jehovah's Witnesses, Sikhs, Catholics, Baptists, Bahai, or Hindus living next door. As long as they obey the laws of this country, they have just as much right to live here as I do.
Oh, yeah. Thanks, Neugier. I agree that any damage to the road caused by Amish vehicles pales in comparison to that caused by semi trucks, gravel trucks, SUVs etc. It's true that the Amish don't pay certain taxes, but then they also don't receive certain benefits, such as Social Security. They also don't typically send their children to public schools.