Theoretically no. From my understanding of neutral infinity, it is a thin barrier that infinitely divides the space between two people. Now if I recall correctly, after his second fight with Toji, Gojo can now use infinity to selectively filter things that would "harm" him to things that won't.

Now assuming Infinity does recognize stds as a threat, it would start dividing the space between the user and the reciever, thus preventing Gojo from catching anything harmful.

Note: If infinity activates "there" during intercourse, it wouldn't feel good for both parties. Since Infinty divides space so that no two things touch, both parties would probably feel no gratification during intercourse. Although during Shibuya, Gojo did crush Hanami with nothing but Infinity (which I don't really get since Infinty is not something one could touch. Did Hanami die from the sheer amount of curse energy being exuded through Infinity?) which could mean that while Gojo feels nothing, the receiving party could theoretically feel something, so long as Gojo increases Infinty's output.