Mennonites are the largest surviving branch of the Anabaptist movement of the 16th century. Although Baptists and other groups that don’t baptize infants owe a lot to the Anabaptist tradition, they’re really quite different and it’s not helpful to confuse Baptists with Anabaptists (as a lot of people understandably do). Obviously on many issues, such as sacramental theology, the Mennonites are radical Protestants. But their doctrine of faith and works is actually closer to Catholicism than that of many Protestants (Lutherans, Reformed, Baptists). In fact, the Reformers thought that the Anabaptists were a form of “new monasticism,” because of their focus on following Christ and taking the Sermon on the Mount literally. While obviously they don’t practice celibacy, this is not such a crazy idea–many modern scholars think that monastic ideals did influence the early Anabaptists. Their most distinctive teaching today is non-resistance–this goes beyond pacifism and historically means that they don’t swear oaths, hold government office, or in any other way participate in the structures of the “world.” However, in many Mennonites today it’s not that different from regular old pacifism.
More conservative Mennonites still have strict rules not only about non-resistance but also about dress and other aspects of daily life. A 17th-century split-off (or, as some would argue, a closely related Anabaptist group) are the Amish, who take these rules much more strictly. But there are “Old Order Mennonites” who don’t have cars, and others who won’t use radios (not to speak of TV). Conservative Mennonite women wear head coverings and dress very plainly. The majority of Mennonites, though, don’t keep these rules any more.