My take is that it has nothing to do with libertarianism. They were operating their buggy on a public road, that road requires certain safety requirements to be met. Those requirements are imposed on all VEHICLES, not individuals. Religion has nothing to do with it. They did not have to use that road (the construction of which also violates their religious beliefs) if they did not want to, they could have found another means or path to their destination, or another destination, but to take benefit of, without conforming to rules of, a public service for reason of religion is a flawed logical argument...it's all, or nothing.
Now, in terms of a personal responsibility, libertarian standpoint, there is nothing that says civil violations for compromising public safety isn't valid, all societies need rules. Are those violations civil in nature? Yes, and so are other vehicle-safety related fines. The CRIMINAL act committed was refusal to pay the fine, and thus effectively claiming the social contract they DID enter into (use of road in exchange for known safety requirements) wasnt valid due to their religion, and even more so, the legal system they also are members of (by being US citizens, and thus enjoying those benefits) also is secondary to their religious beliefs.
Personally, I think this turned out just right...first these Amish citing religion trumps regulation, next step, sharia law. It pains me to link the two, but in this case, the religion-supersedes-law is common to both these Amish, and islamists.