Many of the categories of thought here are very much unique to the modern world and not really applicable to ancient Greece. The category of "science," for example, did not really exist as such. The term "philosophy" was coined by Pythagoras, and what we might now term "science" would have been called "natural philosophy" or "physics". The two plays mentioned were set during the period just after the Trojan war, a period long before the invention of philosophy, and thus neither physics nor philosophy is addressed within the plays.
The only major issue of knowledge has to do with prophecy. As part of a curse, Cassandra's prophecies are not believed. In the case of Creon, a key plot element is his initial refusal to believe the prophet Tiresias. This needs to be seen in a historical context, in which wandering prophets were outside the formal structure of local religion. Although the Delphic oracle was considered a source of authority to other temples, some with associated prophets, official festivals were localized in sacred places such as temples with an official priesthood and civic functions; Sophocles himself was a priest. While the predictions of oracles were held in high regard, they were normally so vague that they had little practical implications. People would interpret the oracles in any way that favored their own causes.
Creon's initial view of Tiresias as subverting his authority suggests first that wandering prophets were looked at with suspicion and, second, that Creon himself was becoming enthralled with power. One should not see Tiresias as part of a larger religious force, but simply as conveying a message from the gods which Creon chose to resist, something that always ends badly in Greek literature.
One cannot really speak of "religion" in the modern sense in reference to ancient Greece. There is not even a Greek word meaning "religion", but rather just the phrase "things having to do with the gods." Much of Greek relationship to the gods had to do with worship, usually offering sacrifices or performing various ceremonies. For a typical family, dealing with the gods might mean offering an oat cake to a god or maintaining a small altar in one's house. In the case of Antigone, the proper burial ceremonies were a duty that one must perform to avoid ritual pollution. The conflict over the burial in the play, though, was not a general issue concerning "religion", but rather Creon forbidding performance of a specific ceremony. This was a highly unusual circumstance and brought Creon into conflict with the gods, leading to his downfall. The conflict from the Greek point of view, though, would not have been between state and church, but rather Creon as an individual using his power to violate the will of the gods. Maintaining good relationships with the gods and performing civic religious ceremonies were important, as the gods, if offended, could send plagues or otherwise harm a city. Thinking in terms of a relationship between "religion" and "political authority," though, would be to misread ancient religion as something far more cohesive than it actually was and as a unified institution and ideology rather than a group of ritual practices.