If I were a man in power and i wanted to protect myself from investing effort into raising children that don't carry my genes, I'd definitely try to establish a taboo around women having sex with multiple partners. And maybe it's possible that if you don't also have taboos around even talking about sex, then the former taboos wouldn't be sustainable. But it seems just as likely that a society that talks freely and openly about sex would be one in which paternity would be easier to establish, because it would be common knowledge which sexual partners a woman claiming to carry your child had.

It seems like it should be a topic covered by Diamond's "Why is sex fun" but I can't remember an exact section devoted to taboos (nothing in the index etc.).