An insightful observation from Bernd G. Längin in Plain and Amish:

All these conservative Anabaptist groups, heirs of identical church reformers, represent something similar to the medieval monsastic system of the Catholic Church. Transplanted into colonial America, they have persevered in living a Protestant ascetic alternative—but without the vow of celibacy.

The Amish ordnung can be compared to a monastic rule of life. Incidentally, early Anabaptist Michael Sattler actually was a Benedictine.