The idea of keeping their culture, especially focusing on Amish, is not as rigid as many think. Many forget that the Amish, as a split off group from the Mennonites already had an immigration phase before going to the US. They came from Switzerland and north-eastern France and were forced to settle into southern Germany because of repressions.
Oddly enough they chose to assimilate with the local populace or at least transplant the ideals of anabaptism, thus adopting the local rhine-frankish dialect, instead of keeping the romansh or french dialects. They specifically chose to not repeat that when coming to America, for whatever other reasons they had.