Today, people cavalierly throw around accusations of Apikorsut to identify practically anyone who doesn't think the identical way as them. Throughout Jewish history, claims of Apikorsut have been behind some of the most vicious character assassinations of celebrated Jewish leaders.
An Apikores is legally defined by Rambam in Hilchot Teshuva 3:8 as:
שלשה הן הנקראים אפיקורסין: האומר שאין שם נבואה כלל ואין שם מדע שמגיע מהבורא ללב בני האדם, והמכחיש נבואתו של משה רבינו, והאומר שאין הבורא יודע מעשה בני האדם. כל אחד משלשה אלו הן אפיקורוסים.
"There are three that are called "heretics" (apikorsin): One who says that there is no such thing as prophecy and there is no such thing as information that is passed from the Creator to the heart of man. And one who denies the prophecy of Moses, our teacher. And one who says that the Creator does not know man's actions. Any one of these is considered an "apikores" - heretic."
Suppose that a reliable person informs you that someone with an otherwise perfect חזקת כשרות has been "teaching Apikorsut". Do we immediately accept the claim and distance ourselves from that person (or even hate them), or is there some process via which the accused's status can be ascertained? And would the process be any different if we had an active Sanhedrin which was accepted by all of Yisrael?
What if there is no way to verify for sure if he had actually taught Apikorsut at any point, and he himself insists that he is committed to these principles as codified by Rambam? Does his own word carry any weight?