Both legally and socially speaking. Even if bestiality itself was not a crime, can't imagine the reputational costs of being widely known as someone who may have defiled last week's dinner were slight.
Another way to put this might be: In pre-Christian Hellenic and Roman cultures, were the Gods generally believed to still actively intervene in the contemporary world as in the legends? Seducing mortals, physically manifesting themselves, directly speaking with people, etc. If that sort of thing was consigned to a bygone age, would claiming you had such an interaction with a god be viewed as blasphemous?
I can at least speak to the legal side. In Athens you could really bring a dike suit (a private suit most likely resulting in a fine) for just about anything you wanted, you just had to be convincing that the action committed is worthy of a guilty vote from the jury. On the flip side, a jury would let a guy get away with anything if they liked him enough or hated the guy bringing the suit. The Zeus defense wouldn't be a good one since many Athenians didn't believe in the gods as direct actors anymore. That could actually backfire, since the Athenian law system believed any unpunished crime resulted in a miasma of bad fortune over the person who committed it until the gods were no longer offended. Rome might have had a law directly dealing with this sort of thing but I'm not sure.