As your question reveals, it is widely believed that sacred prostitution was prevalent in the Ancient World. However, like so much that is common knowledge, the evidence for it is much less solid.

It is true that we have several sources from the ancient world describing sacred prostitution: in Corinth, Babylon, and in many other places. The claims about Corinth have received the most attention from modern scholars for a very good reason. As Robin Osbourne argues in The Oxford Handbook of Ancient Greek Religion - sex in Greek sanctuaries was considered absolutely unacceptable, and therefore the claims made by Pindar about Corinth have been much debated.

Alongside the claims regarding Corinth we have the famous story from Herodotus regarding the temple to Aphrodite in Babylon. But Hannah Wiley argues in the same book that few scholars now accept that sacred prostitution ever existed in these cities. She points out that these tales often stretch plausibility in their details. Lucian for instance provides us with a detailed description of the Temple of the Syrian Goddess at Hierapolis, telling us that it possesses a number of 1800-foot phalluses which are ascended biannually by a man who remains perched on the tip for seven days, without sleep.

As Mary Beard and J. Henderson argue in ‘With This Body I Thee Worship”: Sacred Prostitution in Antiquity’, in Gender and the Body in the Ancient Mediterranean, these tales are often written as salacious tales intended as a practice of ‘othering’ by other Greeks, an argument also presented by Robert A. Oden Jr, who saw sacred prostitution as a literary motive used to denigrate an "Other".

One of the strongest writers on this is Stephanie Lynn Budin, who has attempted to conclusively correct the scholarship on this subject in her work: The Myth of Sacred Prostitution in Antiquity. She argues that the ancient evidence we possesses for sacred prostitution is based entirely on ancient ‘othering’ and modern misunderstanding. She begins her book on page 1 with the blunt claim: “Sacred prostitution never existed in the ancient near east or Mediterranean.” She then spends the book systematically refuting all the evidence that has previously been assumed to support this “myth”.

Budin argues that the overt examples of this practice from ancient authors originated almost entirely from Herodotus, and that: “Herodotus, like all Greeks, wrote about “barbarians” with the intention of proving the superiority of Greeks, and allegations of cannibalism and sexual licentiousness abound. In his descriptions of barbarian sexual mores, he may also have been trying to show the horrible results that could follow if proper women were not kept as guarded and secluded as they were in Greece. All the later Roman and Christian allegations of sexual initiation ultimately derive from this one passage in Herodotus.”

Budin quotes J. G. Westenholz who notes that “Such allegations [of sacred prostitution] first appear in the work of Herodotus (Hist. 1.199) whose view of Mesopotamian culture was considerably biased and whose speculations have been elaborated by Strabo in his Geography (16.1.20), and by other classical authors.” And R. Oden, in his analysis of the literary sources for sacred prostitution, concludes, “What appears to be a list of more than a dozen sources may in fact be a list of a couple of sources, perhaps even and ultimately a single source: Herodotus.”

Budin then moves on to Strabo. She argues that though 25% of historians’ evidence for sacred prostitution comes from Strabo, most of this is a mistake in translation by modern readers who have translated Strabo’s terms such as hierodule, pallakis, and even kataporneuô as referring to sacred prostitution when the language does not refer to any such thing. The only place where Strabo legitimately refers to sacred prostitution is when he speaks of Babylon, and this he derives primarily from Herodotus. Budin argues that: “Strabo does not function as independent, corroborating evidence for Herodotos in this case; rather, the Roman-age geographer merely repeats second or third hand what had been passed down to him in apparently garbled fashion. Strabo appears to be confused about Babylonian sacred prostitution, and his description, as we shall see, betrays his mistrust of the evidence.” Budin refutes the rest of Strabo’s evidence similarly, demonstrating how they derived from Strabo’s confusion over local customs.

Budin finishes her work by presenting a corollary argument, that sacred prostitution was largely a result of 19th century invention, influenced by James Frazer’s work The Golden Bough, itself based on biased Classical sources. She quotes G. Leick: “[T]he ‘sacred prostitute,’ who engages in sex as a magical rite in the context of some fertility cult or officiates in the rites of Inanna/Ištar, belongs to the ‘Golden Bough’ school of historical anthropology.” Budin then presents the argument by J. Assante: “This vision [of sacred prostitution] was largely derived from the 19th century view of ancient Mesopotamia as a forum of naive and primitive sexual freedom allowable before the Old Testament prophets imposed their more austere mores. The notion of Mesopotamia's sexual freedom … was anachronistically based in the 19th century version of it as an exclusively male preserve.”

Selected Primary Sources
Herodotus, The Histories: 1.199

Strabo, Geography: 6.2.6; 8.6.20; 11.14.16; 12.3.36; 16.1.20

Lucian, De Syria Dea: 6

Pindar, Fragment 122

Selected Secondary Sources
Eidinow, E. and Kindt, J., (eds), 2015, The Oxford Handbook of Ancient Greek Religion, Oxford, pp 18, 70

Beard, M. and Henderson, J. 1998. ‘ “With This Body I Thee Worship”: Sacred Prostitution in Antiquity’, in Gender and the Body in the Ancient Mediterranean, ed. M. Wyke, 56–79

Budin, S. 2008. The Myth of Sacred Prostitution in Antiquity. Cambridge.