The Oracle of Delphi in "300"

Uhhhh...so...300 made that up...The oracular individual at Delphi was not a man, but the Pythia, the priestess to Apollo. There is only one possible depiction of her, on a bowl of the so-called Codrus Painter, and that identification is disputed. The selection process of the Pythia is even more poorly understood than the oracular process. In some texts the Pythia appears to generally be an old woman, but in others she is young (c.f. the literary treatment of the Sibyl, who likewise is sometimes young and attractive yet were also said in tradition to be old women who lived to extreme age, prompting Petronius' joke at Satyricon 48, most famously quoted by T.S. Eliott at the beginning of The Waste Land). Plutarch centuries after the Classical Period in Greece wrote that the Pythia was not chosen from the aristocracy, not that that means anything for her appearance, but that's about all we know.

There are quite a large number of divining methods in classical antiquity, so already this question is sort of doomed. Even if we restrict ourselves to just μάντεις and προμάντεις like the Pythia, that is actual individuals, through whom the god either spoke (πρόμαντις) or who were gifted with prophecy of their own (μάντις) the question is still kinda doomed, cuz there's a lot. They do not tend to follow a pattern in the literature. They can be men or women. They can be disfigured and ugly, or exceedingly beautiful (e.g. Cassandra, a real babe). They can be young, old, timeless, all kinds of shit. I suspect that what's being played on is the literary trope common to both prophets and magicians, two categories that often overlapped (e.g. Medea, who is both a diviner and a nasty witch). Often the gift of prophecy (or other supernatural power) is associated in the literature with some sort of physical price. The most famous example would probably be Tiresias, the great heroic prophet (along with Calchas), who is blind. But he's usually just thought of as a regular old guy, he's not particularly disfigured or anything. Another example might be the Graeae, who helped Perseus in his battle against the Gorgons. By Aeschylus' time they were apparently only possessed of one tooth and one eye that they had to share (their numbers, which in Hesiod are only two, have also swelled to three in Aeschylus). But again, to complicate things, the Graeae are not particularly ugly, at least not in the texts. Aeschylus says they were swan-shaped (κυκνόμορφοι, whatever the fuck that means) and Hesiod calls them beautifully-cheeked (καλλιπαρῄους, a standard Homeric epithet for beautiful women) and says that they're well-dressed (Enyo even wears a pretty saffron robe). Further, Hesiod doesn't seem to know about the single eye/tooth problem. Another complicated example is to turn back to Cassandra, who is also charged a price. But her price is mental--in the tradition known to Aeschylus, Cassandra rejected Apollo's sexual advances and was given the gift of prophecy with the curse that no one would ever believe her.

But these are only a few examples of the bajillions of oracular individuals present in the classical texts, many of whom (I would confidently say most, but I would have to check through an awful lot of texts to be able to say that in a paper) aren't old, disfigured, or crippled in any way. Certainly there is no attestation of oracles being selected for physical disabilities or ugliness. Indeed, the Egyptian magical papyri (of the Hellenistic and Roman periods) that deal with spells intended to bind the god to a πρόμαντις for divination tend to prefer attractive young boys as their oracular objects. You're looking at Hollywood, nothing more

I have to say I'm very confused why you think nobody would listen to someone who's ugly...I can think of a large number of unattractive people in extremely important positions of leadership...