Not implying that the Amish & Mennonites are Catholic (by a long shot), but they are Christians and the early Christian church and the Catholic church were one and the same.
Number 2297 of the Catechism, "Respect for bodily integrity," states in part: "Except when performed for strictly therapeutic medical reasons, directly intended amputations, mutilations, and sterilizations performed on innocent persons are against the moral law." In other words, if the baby or child has healthy, normal genitals, or if there is a less invasive solution to a problem than circumcision (such as gentle stretching or use of a steroidal cream), then circumcision -- as an amputation of healthy, functioning flesh with a primary artery and veins -- is not an acceptable choice. All worldwide medical associations agree that elective circumcision is a non-therapeutic surgical procedure, which therefore makes it against the moral law in Roman Catholicism.
This classification isn't surprising, as the Catholic church also forbids tattooing, cremation and other desecrations of the body. However, Pope Eugene IV went even further in clarifying the issue in 1442 at the Council of Florence. He decreed that, "Therefore, it strictly orders all who glory in the name of Christ not to practice circumcision either before or after baptism, since whether or not they place their hope in it, [circumcision] cannot possibly be observed without loss of eternal salvation."
That edict occurred before any Protestant rebellions, so it was intended to apply to all Christians. Most Christians in the world conform and do not practice elective circumcision at all, with the obvious exception of the United States and dwindling populations in other English-speaking countries, Egyptian Coptics, and among Filipinos (for whom it's more of a pre-puberty cultural ritual of unknown origin).
Since the Amish trace their roots to immigrants from Switzerland and Germany in the 18th century, and retain practices from that time, it seems that circumcision would be more or less "off their radar" and be seen as a modern-day US fad among "the English", as they call us fellow Americans.
