Here’s an earlier answer of mine about adultery and the Odyssey, if you’re interested!

• Odysseus has sex with several women (Hecuba, Circe, Calypso) but Penelope remains loyal to his husband. Odysseus' infidelity is not chastised in the story, so how commonplace was this ideology of sex in ancient Greece? Were men expected to be monogamous?

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The Odyssey absolutely and explicitly sets up a double standard, but it's not the one OP's question claims.

In book 5, we're introduced to Our Mighty Hero...sitting on a rock on an island beach, staring at the sea and sobbing. He is somewhere been stranded and an actual prisoner on the island belonging to the "lovely goddess" Calypso. The poem implies that there was some mutual attraction between them initially. But in the years he's been on the island, that has evaporated. They sleep together every night, sure, but Odysseus isn't happy about it. It is possible, although not definitive, to read the situation as coercion/rape.

But this isn't the concern of the poem itself, which doesn't frame this as a "normal" relationship between men and women. Why not? Because Calypso isn't a woman, she's a goddess. When Hermes comes along to pass on the order for her to help Odysseus leave the island, that is the framework with which she protests. From the Penguin Classics translation:

You are hard-hearted, you gods, and unmatched for jealousy. You are outraged if a goddess sleeps openly with a man even if she has chosen him as her husband. You were the same when rosy-fingered Dawn fell in love with Orion. Free and easy yourselves, you were outraged at her conduct, and in the end chaste Artemis of the golden throne rose, attacked him in Ortygie with her gentle arrows and left him dead. And so again, when the lovely Demeter gave way to her desire and made love with her beloved lasion in the field of the three ploughed furrows, Zeus heard of it quickly enough and struck him dead with his blinding thunderbolt.

The contrast with, of course, Zeus is clear. Calypso gets to essentially denounce all of Greek mythology as sexist, even if it is not a sparklingly feminist message today.

"Adultery" in the traditional sense, thus, is not the issue in this case.

That said, K.J. Dover and other scholars are exquisitely clear that under Athenian law (to be fair, not necessarily the situation reflected by tradition of singing the Odyssey), adultery with citizen women was very not okay for men. Naturally, it was a crime committed not against morality or the polity, but against a specific man who had legal control of the woman involved:

But Greek laws were not lenient towards adultery, and moikbeia, for whch we have no suitable translation except "adultery," denoted not only the seduction of another man’s wife, but also the seduction of h s widowed mother, unmarried daughter, sister, niece, or any other woman whose legal guardan he was.

Dover adds that adultery was considered worse than rape, because rape was considered a crime of passion and the moment whereas to carry on an affair involved seduction--that is, a long period of time and effort. Xenophon's Hiero, which is more or less a work of political philosophy, compares the two:

At any rate, it is not uncommon for the laws of communities to allow people to kill seducers, and only seducers, with impunity, and the thinking behind this law is obviously that seduction impairs the affection a wife feels for her husband. After all, if sex takes place without the woman’s consent, this does not make the slightest difference to the regard her husband feels for her, as long as the affection she feels for him remains inviolate.

Now, it's important to keep in mind that we're dealing primarily with normative or prescriptive sources here, not descriptive. (And Xenophon, for his part, is exaggerating a bit for rhetorical effect, as Edward Harris points out--seduction/adultery was by no means the only crime for which one could be executed.) The cuckolded man was afforded, in theory, a significant amount of say over how/whether the philandering man was punished. So even under the law, there would be a lot of room for flexibility or ambiguity in what actually happened.

However, more literary/normative sources are particularly useful in reflecting one aspect of the situation: being seen as an adulterer was not good. The fama for such men would swirl with scorn and satire. Dover suggests that because women were seen as easily seduced and swayed by temptation meant that adulterers rather than the cheated-upon received the brunt of social derision.

But just as we have to consider the context of Odysseus sleeping with (under ambiguous terms of consent) a goddess, the status of women in relationships outside marriage also mattered. For example, enslaved women were subject to rape by their owners and by whomever their owners gave them to as a "gift."