To my knowledge, the story is (Graeco-)Roman in origin, written early in the first century CE by a Macedonian poet at Rome. It occurs in Phaedrus' Fables 4.16, and it is Prometheus (not Apollo) who is responsible for mixing up people's genitalia while making them from clay. The fable 'explains' the origins of tribades women and molles men, so of women who behave in male ways and like penetrating others, and of men who are soft and feminine and like being penetrated.

This is the Loeb translation of the fable:

Someone else asked him what natural cause had produced tribads and effeminate males. The old man explained: “The same Prometheus, author of our common clay (which is broken as soon as it clashes with Fortune), had all day long been fashioning separately those natural parts which the sense of shame causes to be hidden by our clothing, that he might presently apply them to the proper bodies, when, quite unexpectedly, he was invited out to dinner by Bacchus. There he absorbed a great deal of nectar into his veins and returned home late in the evening with wavering steps. Then, with sleepy head and drunken fumbling, he fastened female parts on bodies of masculine sex and masculine parts on females. Hence lust now gratifies itself with a perverted pleasure.”

Tribades and Molles are not neutral terms, but terms used to brand and wound. The discourse on sexual and behavioural 'abnormality' is deeply normative and moral, with its aim clearly being conformity. This conformity was thought to be visible in hair style, personal grooming, behaviour and presence in certain spaces.

In the fable, it seems that Phaedrus' view may have been that in such cases gender identity and sexual desire are both at odds with the person's physical body. Physical appearance is hence treated as an unreliable sign of gender, but behaviour reveals true inclination. Phaedrus hence seems to be playing with the normative boundaries of gender roles and the generally held assumptions about how they functioned (or he may be responding to changing discourse in the imperial period).

I would not say that Phaedrus is typical of ancient discourse on gender roles, nor is he necessarily indicative of a conscious awareness of trans experiences in the modern sense, but I welcome corrections to my view by those with more knowledge on the subject. Molles and Tribades are hostile terms for groups that may have included persons going through what one might call a trans experience, but they certainly included many who did not.

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Some bibliography:

Kristin Mann, "Reading Gender in Phaedrus' Fabulae", in: The Classical Journal 115:2 (2020), 201-227.

Doherty, Lillian, Gender and the interpretation of classical myth, London 2001.

Hallett, Judith, “Women as 'Same' and 'Other' in the classical Roman elite”, in: Helios 16:1 (1989), 59–78.