“Let’s say one or both partners are infertile and want to practice unprotected sex. Both partners have been tested for STDs and are clean. Is it safe to have unprotected sex, or is it possible to get STDs even if neither partner has one?”
If both partners are negative for any STI, then as long as you remain mutually monogamous (neither person has sex with anyone else) you cannot get a sexually transmitted infection.
As a reminder, there are several STIs that are transmitted by other body fluids, such as blood or saliva (HIV and Hepatitis) so high risk behaviors, like IV drug use, would put both partners at risk.