In some ways the ancestors of the viruses and bacteria that cause these predate the more complex life they infect today. These microorganisms were here long long before multi-cellular life, and as multi-cellular life has evolved they have evolved along with it for ways to infect and transmit between hosts along with how to evade the evolving immune systems of the hosts.

In terms of STDs, this is a very close contact between two individuals and normally involves contact that avoids the hardier skin that’s on most of the rest of our bodies that’s a better (but not perfect) barrier against infections getting through. So a good transmission route, albeit often not for immediate mass infections like influenza or measles.

So as sexually reproducing species evolved these viruses and bacteria were there already, and grew up alongside us using this fairly reliable infection path to spread.