In political science, the definition of "conservative" includes definition to the effect "honors and values traditional, established, customs, norms, practices, standards and behaviors." Other definitions may include "suspicious of, and slow to accept, social, religious and other change." This is why most conservatives would oppose homosexual marriage, for example.
You have termed this philosophy "out-of-touch." Others might apply "old-fashioned" or similar descriptions. So yes, in answer to your question, Amish, Mennonites and others who are wedded to "traditional, established, customs, norms, values and behaviors" really are conservative and would thus likely vote Republican.
An interesting exception is American Muslims. They are certainly religiously, socially and often even appearance-wise highly conservative in their behaviors, at least according to their homeland and religious traditions. Yet they vote Democrat. Why? Because they believe that Democrats are far more tolerant of them and more likely to accept them than Republicans. Today, this is even more true, because Pres. Obama, although a long-time Christian, was raised by Muslim fathers in Muslim countries for a time, and American Muslims believe that he has a better tolerance of Muslim culture, society, beliefs and practices.
12 years of teaching college political science.