I don’t know the answer, OP.
But the attitude of Christianity towards eroticism is indeed on the ascetic side, and has been since St Paul, and arguably Jesus himself (if you look on someone with lust, poke your eye out). The attitude towards the naked body would follow suit; and of course the Games were explicitly a pagan religious ceremony anyway, which was reason enough to ban them.
Jews are happy to point out that Judaism’s attitude towards sex is much healthier than Christianity’s: where Paul barely tolerates matrimony, the Talmud enjoins a healthy sex life as a conjugal obligation.
It’s not as simple as that; but the Song of Songs is neither here nor there. Yes, when it was composed the Song of Songs was erotic; Wikipedia points out parallels with Mesopotamian and Egyptian love poetry, and the suspicion of an allusion to Tammuz and Ishtar. But Judaism, let alone Christianity in the 4th century AD was not the proto-Judaism of the 10th or 6th century BC, when it was composed. The Song of Songs was only accepted into the Jewish Bible in the second century AD (!), and that only on the condition that it was an allegory for God’s love for Israel:
For instance, the famed first and second century Rabbi Akiva forbade the use of the Song of Songs in popular celebrations. He reportedly said, “He who sings the Song of Songs in wine taverns, treating it as if it were a vulgar song, forfeits his share in the world to come”.
The Talmud’s treatment of Epikoros is a rejection of Hellenistic hedonism, for which Epicurus is the poster boy (fairly or not). For all the disjonts between Judaism and Christianity, I’d have thought Jews and Christians would be united in looking askance at nudity in the Games.