As fascinating as what one had to do as part of the cult of a god, is what one could not do.
In 'The Elgin Marbles' I covered the scandal Demetrius Poliorketes caused by keeping his whores in the Parthenon. These were not religious objections - it was okay for Demetrius to sleep with the women there, because the Parthenon was not a temple. The Parthenon did not house the cult of Athena until the Late Antique period - for most of Antiquity her cult was housed in the Erechtheion. Sex in Greek temples was banned, and the Athenians were quite scrupulous in adhering to the sacred laws; they changed the names of the months to allow Demetrius to be initiated at Eleusis in the 'correct' month, for example. Exceptions were made at a few cults of Aphrodite, but that's another story.
Xenophon's biography of Agesilaus makes it clear that the Spartan king did not wish to be accused of any improprieties, so he slept in temples when traveling (5.7).
Herodotus tells us another story that illustrates how sacrilegious the Greeks thought sex in temples was (9.116-20). During the Second Persian War Artaykes captured the Chersonese, and set up house in the shrine of Protesilaus at Elaeus. (Protesilaus was the first Greek killed at Troy) The Persian looted the treasure, and slept with women in the shrine. He justified his looting to the king by claiming he was only taking back from the Greeks had taken from the Persians. The Athenians captured the shrine, and Artaykes tried to bribe them with its treasures. Instead, as punishment for having defiled the temenos, they crucified him. His son was stoned to death - he hadn't had sex in the sanctuary.
We know that births and deaths were not allowed in Greek sanctuaries (Asclepius as a medical cult may have been an exception). The whole of Delos was dedicated as a temenos to Apollo, and Delians had to leave the island to give birth or die. I assume that Delos made an exception for procreation.
So what about Christian claims of orgies at the Eleusinian Mysteries ?
Whilst most religion was public, where cults involved the revelation of a ‘secret’ the rites were a closely guarded secret. The Eleusinian initiation Mysteries were such a secret, and Roman historians did not write about them to avoid sacrilege. Although the stigma attached to discussing the Eleusinian Mysteries faded over time, in the second century AD Pausanias would not even describe the buildings within the sanctuary at Eleusis, omitting them entirely from his Guide to Greece. Well into the Byzantine era the name of the chief priest (the hierophant) was neither written nor spoken out loud. The secret ceremonies of Demeter and Persephone have to be pieced together from brief mentions and passing references over the centuries, just as the Telesterion in which they took place has been pieced together from a series of architectural elements excavated from the ground.
Much of our knowledge comes from the writings of the early Church Fathers such as Clement of Alexandria, who attached no taboo to writing about Eleusis. Since the Christians were against pagan mystery cults – they would rather people went to Mass - one naturally has to take their claims with a very large pinch of salt. Their allegations about various temples and cults range from human sacrifice to ‘sacred marriage’ (hieros gamos), used as a euphemism for orgies. Early Christian writings about the pagan were expressly designed as propaganda. Since the writers were Christian, they almost certainly did not belong to the cults they describe, instead repeating information heard third-hand. It is highly unlikely that orgies were ever held in the Telesterion at Eleusis, as Asterios Bishop of Amaseia claimed – ritualised sex was not part of the cult of Persephone.
Apparently Asterios’ orgies took place in tunnels under the Telesterion, but the building has been excavated down to bedrock and the tunnels do not exist. They were a product of his fertile imagination. The archaeological remains of the Telesterion, the main cult building at Eleusis, do not suggest that the building was conducive to orgies. Ancient architectural design was entirely shaped by its purpose: brothels had stone beds; dining rooms had doors that were off-centre to accommodate couches; and libraries double-shell walls to keep out the damp. As a result, most ancient buildings are architecturally distinct and easily recognisable in excavations – since there was no practical place to hold these orgies inside the Telesterion, it can categorically be stated that they did not take place in it.
The Haloa was a fertility-related Eleusinian festival of Demeter, whose use of phalli may well have influenced the Christian writers. Its ‘naughty’ nature is well attested but, unlike the Mysteries, it was restricted to woman; orgies are unlikely to have taken place as part of it, as men were not present.
Still, the slander has stuck - Greek men still use the suggestion of “going to Eleusis” as a euphemism for casual, meaningless sex.