an ALCA church nearby and I have never heard of this group before.
They are also known as the Laestadian Movement. Though having the name “Lutheran” they hold a “quatenus” subscription to the Augsburg Confession, that is they accept it only in so far as they believe it agrees with Scripture. This view of confessional [non]subscription really makes a confession of faith meaningless as it subjects the confession to the ever changing whim of personal interpretation of Holy Scripture (which the ALCA does regard as the inspired Word of God). The Apostolic Lutheran Church / Laestadians are largely a lay movement, that is highly pietistic, emphasizing a conversion experience. Most congregations have lay preachers, and they are noted for their abstinence from alcohol.
We have recommended the novel Hammer of God by Bo Giertz before. In the novel similar Scandinavian pietism comes up. In it you can see both the appeal and the theological shortcomings of this theological view.
Matthew Lorfeld, Pastor
Messiah Lutheran Church
La Crescent, MN
To learn more on the subject of Pietism: