amish usually don't vote as they see it as part of the outside world.
Most don't vote, but the ones who do generally vote Republican.
Yeah, and having been to the area on a vacation, the Amish culture is a huge part of the life for the non-Amish. They have a bunch of tourism based on the fact that they're "Amish country." You see tourist slogans like "Elkhart County - Old Fashioned Values" and "Cozy. Just like Home." There is a strong sense of nostalgia when you go there, and the label "old-fashioned" is used everywhere there. The area really lends itself to strong social conservatism, and as Thomas mentioned, the Amish themselves are deeply conservative.
And in some of these counties the percentage speaking Pennsylvania Dutch is quite high - nearly 30% in LaGrange County, for instance. So Amish political influence is rather strong in those parts of the country, even if indirectly.
http://en.wikipedia.org/wiki/LaGrange_County,_Indiana