I found it incredibly difficult to get a specific explanation of why circumcision prevented the spread of STD's, explicitly HIV. It's an issue in Africa where they push circumcision quite heavily, even on adults, in order to combat AIDS, and it involved all the same arguments that you would normally hear in the US about cleanliness (where at least in Africa, this makes much more sense).

It actually took me a while for someone to finally talk about the actual biological and virological mechanism (especially considering how small the virus is, and we're still assuming both parties are engaging in sexual intercourse anyway), rather than just pointing at a statistic and saying "but probability go down?"

It's been a while, but as I recall, it had something to do with the fact that the exposed area under the head of the penis actually has pores that emit smegma, and the smegma actually allows the HIV virus to be active longer, and enter in through those pores, even after sexual intercourse has already ended. So the issue is that basically, a circumcision might reduce smegma buildup and also allow your dick to basically dry out and the virus will be less likely to survive with less moist and beneficial habitat. That is why it can reduce HIV transmission.

However, all of that was not common even readily available knowledge. For the most part, people are just pointing at a statistic and saying "number go down", without understanding why.