Counterpoint, a congressman released a sex tape of himself with a prostitute.

I've never heard of a man getting fired because someone stumbled across his nudes - not saying it's never happened, but it doesn't happen much. I've heard of plenty of female teachers getting fired for it, but also female office workers.

It seems like there's this idea that being able to see a woman nude somehow discredits her and undermines her authority. The same idea doesn't exist for men

And I'm pretty confident that you could post nudes online, and even if someone found them, it wouldn't end up with you ending up in HR or having to justify yourself... Maybe you could have personal complications because of it, but probably not social ones

I think it's at least hyperbole. The consequences aren't the same, aren't even equivalent, but there are still negative consequences.