As far as I can tell, the Amish are not Luddites. They don't reject technology per se.

It is more of a form of voluntary (/community imposed) self denial. Thus the flexibility.

Ferinstance, Roman Catholics in the US are bound to abstain from eating meat on the Fridays in Lent. Its not that we think there's something evil about eating meat - its just an arbitrary sacrifice, an exercise in mortification.