What do you mean by can monogamy survive? Do you mean that in a world without STDs it would be abnormal for someone to expect an intimate relationship to be exclusive?
The intimate relationship is one component of monogamy, there's also having a steady nearly guaranteed sexual partner with low risks.
Ideally you're both monogamous so unless one had STIs before entering the relationship, it's incredibly unlikely either would acquire one and almost certainly not from intercourse but through some other means.
There are people more interested in the low risk stable sexual benefits of a trustworthy monogamous relationship. I personally doubt it's more than the number of people wanting an intimate relationship beyond sex though.
