As far as I know, there weren't any significantly life-threatening sexual diseases for most of human history in most of the world. Syphilis only affected the Americas before the 1500s, and HIV is much newer than that.
Most other sexually-transmitted diseases that existed in most of the world were unpleasant, but not life threatening, even before antibiotics. And it's also worth noting that most primates (and many mammals of all kinds) are not monogamous, and yet they are not plagued by STIs to any significant extent.
Instead, monogamy was much more important for managing babies, especially given how much hare human babies need, and for how long, compared to virtually any other animal.
Syphillis isn't from the Americas or anywhere specifically. It just gets described in European literature around the time of Columbus first documented contact. If you read descriptions of literature from that time it's either a separate virus or the virus mutated radically since then to become less fatal.
As far as primates not having STIs, you might want to read up on the animal origins of HIV a bit. The only reason we have HIV is because SIV can proliferate indefinitely in another species and crossed into humans.
It looks like the European strain wasn't as deadly as the American strain. Pre-Columbus skeletons showing signs have been found.
However, with a slow disease like syphilis there's also the issue of how well it was identified in old times. Identifying the primary form as sexual is very different than identifying the tertiary form as a continuation of the primary. It was 1965 before we realized shingles is tertiary chicken pox and the 1980s before they realized that cervical cancer is mostly tertiary HPV. Other virus/cancer links have been identified (I recently read that IIRC 5% of cancer is known to be of viral origin) and personally I think the actual number is even higher as determining a link between an asymptomatic virus and later cancer would be very hard. (Again and again I see news reports of clusters of unusual cancer where no cause is found but the pattern looks contagious. It's very hard for cancer itself to be contagious but the same effect would be observed if the cancer was due to an asymptomatic virus. I also find the notion that random mutations could cause consistent behavior of the cancer strange--but quite sensible if it's viral damage.)
As far as I understand, the exact history of syphilis is still unknown, and the idea that it was spread to Europe from the Americas is not completely impossible (though seems less likely today).
As for SIV, I am aware of it, but it is not a serious problem for most simians (though apparently Chimpanzees are being killed by SAIDS in serious numbers) - which is my point. STIs have not been so serious a threat to animals as HIV+AIDS has been to humans in the initial pandemic.
Most other sexually-transmitted diseases that existed in most of the world were unpleasant, but not life threatening, even before antibiotics. And it's also worth noting that most primates (and many mammals of all kinds) are not monogamous, and yet they are not plagued by STIs to any significant extent.
Instead, monogamy was much more important for managing babies, especially given how much hare human babies need, and for how long, compared to virtually any other animal.