Sort of both, I live in central Pa, lots of Amish and Mennonites. They are very strict when it comes to religion, even worse than most fun dies, but are very nice people for the most part and aren't really pushy about religion unless you bring it up.
Both. They are Christian and highly religious, but they are also culturally unique. I have friends who belong to various Mennonites and Brethren groups, and it's interesting to note the difference between them. Anyhow, they're clearly different from the predominant culture around them, and also have their own way of practicing their Christian faith. On the whole, I've had good dealings with Mennonites. They've always been nice to me despite the fact that I'm not one of them. Also, they have some very good charitable organizations.
They are sort of a religion and a culture. They have their own religion, which is a reform Christianity, which most of them follow. But I don't think "Mennonite" in and of itself is a religion, but a way of life.
But they are also a culture, as they have their own unique celebrations, milestones, day-to-day life, values, norms, mores (pronounced morays, see: sociology), and in some cases, their own language (which is sort of a German/english hybrid, in southwestern Ontario anyways. I think there's a name for the language, but can't remember it).
So, it is a culture, but it is a culture which centers around a religion. Religion-based culture, perhaps would be the best way to put it.
Mennonites derive out of the Anabaptist tradition, which can be described as being to the left of the Reformation, meaning this tradition developed because they believed that Christianity was aligning itself too closely with the politics of the State. They teach non-violence in relation to "the third way of Jesus". They would classify themselves as pacifists, but since most people don't understand that term and think "personal", the term "active peace building" could be a better term to describe their beliefs.
Today, the Mennonites have a huge following within Christianity in the U.S. and have contributed theologically in incredible dynamics. One of the best Mennonite theologians is John Howard Yoder, who wrote, "The Politics of Jesus". Christianity is overall a religion as well as culture, it is impossible to separate the two.
Mennonite is a term used for a variety of Anabaptist Churches. Mennonites are named after the Dutch Reformer and former Catholic Priest Menno Simons, Simons rejected the Catholic Church and it's priesthood and the idea of infant baptism.
Mennonites vary from those resembling the Amish AKA the Old Order Mennonites (the Amish split back in the 1600's) to people who dress like other Americans.
Mennonitism can be BOTH a culture and a faith as some Older Mennonite groups shun outsiders and keep to themselves. On the other hand I myself attend a Moderate Mennonite that is very modern and has contemporary music and that is very friendly(I have been attending Solid Rock because the Messianic Jewish Synagogue I was attending moved and is now 100 miles away! But what a wonderful blessing Solid Rock has been.!)