What are the precise criteria for classifying a statement or a school of thought as "shādhdh" (aberrant) and "munkar" (repudiated), such that it is censured for its proponent and follower?

The judgment on the sayings or doctrines of scholars as being an anomaly (shudhudh) or objectionable (nakārah), and that it is impermissible to follow them, is the prerogative of scholars deeply rooted in knowledge, those who are aware of the differences among scholars and the reasons for their differences. As for the common person, they must follow someone whose knowledge and piety they trust, and ask them about what is unclear to them concerning their personal religious matters.