None of the classifiers in q2-feature-classifier generate "random" results or give different answers each time you run them, unless if you change the reference sequences... or if there is something wrong with the query sequences, e.g., they are in mixed orientations. This topic links to a few different discussions of taxonomy and unclassification issues, you could browse those if you think that variable classification is the issue.
Evidently something was removed — why do you doubt it? I recommend starting there to verify whether or not any sequences failed to insert with fragment-insertion.