Educate me. What is the Old Believers theology? I know about the two fingers, not much beyond that.
OB theology is Orthodox.
OBers have no episcopate. So they got their priests from the ROC before the 1925. After 1925, they got them from the ROCOR.
OBers rejected the 18th (?) century liturgical reforms in the ROC, but they did not reject the ROC as such.
Communities that still exist, exist without benefit of clergy. They have saved some of the consecrated Holy Mysteries, but only the Body, and manage to consume just a few Crumbs to make It last. I have heard a community in Erie, PA finally became reconciled to the ROCOR some years ago. Other communities exist in Siberia and Alaska.
Because of the lack of clergy, some of the communities have gotten a little goofy, so I hear. According to Thurston and Attwater, for example, some OBers believe in the Immaculate Conception.
OBers are greatly respected by the Orthodox and their icons are prized.