Autosomal DNA (atDNA) testing is all the rage these days. Webinars, conferences, and lectures all tout the benefits; but if you are of Mennonite descent, should you be so excited? My answer is, generally, no. Low German Mennonites have been a highly endogamous people until recently, and atDNA is very difficult to use with endogamous groups.
A few definitions - autosomal DNA is the DNA on your 22 pairs of chromosomes that come half from your father and half from your mother. This DNA test is used to find stretches of identical DNA that you likely inherited from any of your ancestors. Here is a wiki with more information.
An endogamous group is one that has mostly married within itself for a long period of time. As a result, members of an endogamous group are related to each other in many different ways. You can inherit pieces of identical DNA from multiple ancestors and thus appear to be related much more closely to someone than you really are. For example, my parents are 3rd cousins once removed in two different ways, 4th cousins, 5th cousins, and 7th cousins once removed. And these are just the ones I know about.
For example, I have Klaas Johann Siemens #46557 (ABT 1758-1834) as a 3-greats-grandfather on my mom's side and a 4-greats-grandfather on my dad's side. This is one of the relationships that makes them third cousins once removed. Very likely Klaas Johann Siemens passed the same piece (or several pieces) of DNA to me via both my dad and my mom. If I have a DNA match with another of his descendants, it looks as though we are much more closely related than we really are because I am getting DNA from two paths from Klaas Johan Siemens, not just the normal one path from one parent. And then when you have several of these kind of relationships in your ancestry, it really starts to add up.
So someone who appears to be a 2nd cousin based on the amount of shared DNA might really be a 4th or 5th cousin or even more distant. In fact, I have a number of matches that are supposed to be 1st and 2nd cousins (based on DNA testing) whom I know are NOT actually 1st and 2nd cousins. It would require the testing of many, many cousins (probably dozens or scores of cousins) to untangle all these relationships.
In my personal case, I tested at 23andMe in 2012, and I think it was a waste of money. I also uploaded my results for free to Gedmatch. Neither produced any genealogical results.
There is one case where atDNA would be useful for someone of Low German Mennonite descent. If you are searching for a recent ancestor, say a parent, grandparent, or great-grandparent, then it would be worth doing. This would occur in cases of adoption, recent non-paternal events, or if your family has lost information about the most recent generations. You will still get results that show matches who are supposedly more closely related than they actually are. But these are easier to work through for recent generations. And you may not have any other good options for doing research.
In the comments please share your experiences, positive and negative, with atDNA.