Amish people DO ride trains, especially for long distances.
I used to live among (not with) the Amish in Pennsylvania. The ones I met were shy and reserved, but sometimes they are very happy to have us talk to them.
They are a distant and proud people. I don't agree with their religious beliefs, but I am amazed that they stand so steadfastly with their beliefs. I admire them, but I would not want to be one.