This practice dates back to the colonial era, according to John Hostetler. From Amish Society, p. 234 (footnote 1):
The Amish practice of calling outsiders “English”…can be traced to language and ethnic-group differences in colonial times. Compact settlements of Germans were distinguished from the English, French, and Spanish colonies in the New World. The Germans did not have a colony, so when the English spoke of Amish and Mennonite groups, they simply called them “Germans.” Today, when an Amish person calls someone an Englischer, it does not imply any disloyalty to America; it simply indicates that the person is non-Amish.
Not all Amish use the term “English”, however. In this video I give examples of other things which the Amish call non-Amish people. This can vary by community, and by which language the Amish person is speaking.
I remember getting a kick years ago out of learning that Amish call non-Amish Americans, myself included (having zero known ties to England or anything close to it), “English”. But if you live in one part of Ohio, for example, they call you something else. Runtime: 3:59.