Given that ancient Greece did not have sacred books, as in the Abrahamic religions, what value did texts such as the Homeric hymns, Hesiod's Theogony, the Library of Apollodorus, the Dionysiaca, etc., have?
The difference between ancient Greek religion and the Abrahamic traditions is that Greeks had authoritative religious/cultural traditions but no authoritative scripture. The "authority" was τα πάτρια, aka, "the ancestral customs", and sometimes cults, oracles, and temples where the clergy could give some direction and knowledge.
The texts you mention occupied different positions, and none of them functioned like the Bible or the Qur'an. Long before anyone wrote the Theogony or the Homeric Hymns, stories about the gods were already circulating orally. So the written works themselves were not revelations, but records of pre-existing traditions. A Greek hearing Hesiod would not think: "This is true because Hesiod wrote it." but "Hesiod is telling the stories of our gods."
Of course, each work had a different purpose. For example, the Homeric epics where teaching/didactic. They could teach the people about the personalities of the gods, heroic ideals, religious customs, and moral examples. That doesn't mean Greeks believed Homer was infallible or the only source for information about the gods. But it is one of the most informative texts for the Greeks about the gods to this day.
Hesiod's Theogony, on the other hand, attempted an organized genealogy of the gods. It's also a good text to rely on because it's a more systematic source. However, this was not supposed to stop other Greek poets and ordinary people from writing down the versions of the genealogy they knew from their own region and traditions.
The Homeric Hymns were not "scripture" either. They were a response to the existing knowledge about the gods. Like our hymns today, they were a way to worship the gods and also pass down the knowledge of the people about the gods and their stories. They were sacred literature, not sacred law.
Apollodorus' Library is a very late work (probably 1st–2nd century CE) by an unknown author, conventionally called Pseudo-Apollodorus. Its purpose was that of a handbook, as it summarizes myths from many earlier sources. Ancient scholars valued it because it collected traditions, not because it carried divine authority.
Nonnus' Dionysiaca is an even later (5th century CE) and it's certainly not considered "religious scripture". We have the advantage that we can learn traditions and stories through the epic, however it didn't mandate how one **should** see Dionysus.
If a certain written work described a myth differently from your city's tradition, your city just kept doing what it had always done. For example, one city might insist a god was born there, while another claimed the same honor. Both traditions could coexist without needing to decide which was "correct." That's why contradictions were accepted. Thus, a hero might have different parents, adventures and deaths depending on who told the story. People rarely felt compelled to eliminate every inconsistency because they just followed their local customs.
This is not a unique condition. Customs can overrule religion in most countries around the world - if not in all of them.
