Random Access asks:

No concept of heresy? Wasn’t Socrates put to death for being an atheist though?

It’s not quite the same thing.  Denying the existence of the gods altogether is a problem for them, although in Socrates’ case that was probably just a pretext to get rid of him (as far as we can tell, he wasn’t an atheist at all, at least not in the sense that we understand it).  The late antique and mediaeval notion of heresy, though, presupposes that there are wrong and unholy things to believe about God(s), or wrong and unholy ways to worship God(s), even if no one disputes that he/they exist(s).  For instance, for a 4th century Christian to say that God the Son is inferior to God the Father, when the central authorities of the church believe that they are equal, is heresy (specifically, the Arian heresy) and can get you excommunicated.  There isn’t really any equivalent in the polytheistic religions of the classical period, because they have no dogma and more or less take it for granted that different communities have different ideas about what the gods are, how they act, and how they should be worshipped.

EDIT: An illustrative example.  Hesiod’s Theogony says that Aphrodite was born from the blood of Ouranos, the primordial sky god, when it mixed with the foam of the sea.  Homer’s Iliad says that Aphrodite is the daughter of Zeus and a minor goddess named Dione.  These are two fundamentally incompatible origin stories for one of the most popular goddesses in the Greek world, and they come from the two most respected and authoritative Greek poets.  You can believe either.  Or neither.  Or even both, if you can wrap your head around it (that was Plato’s answer).  No one particularly cares.

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