We don’t know of any group either Mennonite or Amish that outsiders can’t join. The question is rather if the outsider is truly willing to meet the requirements of the faith. The Old Order Amish have few modern Americans joining them, and the average American would probably say it’s because the Amish are too strict. The Amish bishop would say it’s because the average American is unwilling to submit to the demands of the true Christian way.
The outsider would have to give up a lot of things that they are used to, and learn a lot of new things, almost like moving to another country. He/she would need to immerse themselves into the culture of the Amish and their rules, learn German, learn to live without electricity or a car, and much more. The Old Order Amish are still growing very quickly, despite the fact that not many outsiders join them, because they have so many children, and few leave the Amish culture.
Information provided by "20 Most Asked Questions about the Amish and Mennonites," by Merle and Phyllis Good.