I think he has a point about how culture affects relationships, and many schools of thought believe monogamy developed as a means of controlling women's reproduction to enable to men to control assets. In many parts of the world extra-marital affairs aren't viewed in the same way as here in the UK and aren't considered particular dealbreakers.
However, I think that's rather missing the point.
Weiner lives in a culture where married monogamy is considered the building block of society. As a representative of the people he is supposed to be whiter than white. He deserves to be held accountable for his actions for the simple fact that he has displayed devastatingly bad judgment. A politician who indulges in sex chats is a fool. If he was arrogant enough to believe his privilege would save him from being exposed, he doubly deserves his fate.
His wife may have fallen for the BS but equally she may have chosen to stay married because it confers a political advantage to both of them. That choice is hers.
If it were me, however, I'd walk. Once may be forgivable (arguably) but twice just displays a breathtaking lack of respect for her. Monogamy may be an artificial social construct, but no one needs to conduct lurid sex chats to achieve personal happiness and if you sign up for a monogamous relationship in marriage, then that's what you sign up for. If you can't do it, don't get married.