I think we got to a conclusion – this thread is more about what is in the mind of the OP than of the objects. Avira seems to suspect that everyone who is not thinking like him is an apikoires, and the fact that the person read or quotes some T’Ch not approved by Avira as the definite proof.
We indeed have a mishna that lists cases where we correct shaliach tzibur when he _expresses_ inappropriate beliefs, I just don’t see tanna going as far as Avira does.