In cryofibrinogenemia (not cryoglobulinemia), what is more likely---the condition incites an autoimmune reaction due to inflammation it causes, or an autoimmune process causes the cryofibrinogenemia?

Disease then CF. Cryofibrinogenemia is an unusual finding that usually signifies an underlying disease process. It may be autoimmune, but is also associated with a host of other disease including malignancies, infections and medications. Sometimes it is a benign finding in an otherwise healthy person.
Depends. There is a primary/essential cryofinrinogenemia or idiopathic and there is a secondary cryofinrinogenemia that can be caused by different things like infection, autoimmune/connective tissue disorder, malignancy, cryoglobulinemia etc.