Gaius had learnt long ago that if he didn't charge for his services then people would see him sooner, and he would be able to save more lives. He also knew he had to make it clear he never gossiped and never judged.
These were the reasons why Gaius, more than any other court physician dealt with STDs. There was no prevention and only cures, so he had to get people to come to him. And when a women fell pregnant he made sure to talk them through all their options.
It was two years after Merlin first came that Gaius decided enough was enough and he'd have to examine him. Merlin had never been to see Gaius about any sexual health problems, had never gotten a woman pregnant. Yet he was sexually active. So he ambushed Merlin when he came in one evening late and muddy. Ordering him into a bath and then an examination.
It was all negative, Merlin was fit and healthy. Six months of study, tricking Merlin into sleepy with people he knew were sick (but completely curable), having him care for the highly infectious and Gaius could only conclude Merlin could get sick but not STDs.
Gaius surmised this was because Merlin enjoyed sex and felt it to be something natural and good, his magic kept it safe for him. But how could Gaius use this? Prevention is better than cure. He mulled over this problem for three and half months. Noticing that those who Merlin slept with never became sick again or pregnant unless they wanted to.
HE confronted Merlin one day who sheepishly admitted that when he mother had first spoken to him about sex and what symptoms to look out for he had been scared and panicked. It seemed that Merlin had cast a spell on himself. And if an untrained idiot could then why not a fully trained physician who actually knew something about magic.
Realising that he couldn't cast a spell on every person, far too dangerous and he didn't have the magical strength. Gaius visited Camelot's water supply. The water would hold the spell, he wouldn't need much magical strength and everyone would be safe. A short incantation later and Gaius left satisfied Merlin wasn't the only with magic who cared about this city.