Contracting incurable sexually transmitted infections or diseases (STI's or STD's) would affect relationships physically, emotionally, and legally. Physically speaking, engaging in sexual activity with a partner who has contracted an STI carries varying amounts of risk. One is of course the risk of spreading the disease or infection to the unaffected partner. Though the spread of some STI's (such as HIV) can be prevented through the use of a condom, there is always the risk that this barrier will fail, either from improper use or the very rare instance of defect. Also, there are some STI's for which spreading is not prevented by the use of condoms. In these cases, sexual activity is not advised at all for the infected person.
In addition to the risk of infecting one partner, there is an added risk infecting a fetus, if a pregnancy occurs. Very severe cases of herpes in a pregnant female, for example, come with a heightened chance of birth defects in the fetus. Add to these the physical affects of the diseases themselves. Though many lie dormant, or are at the very least, controllable, almost all STI's have the potential for serious enough health effects that a sexual relationship would be directly impacted.
In addition to physical effects, there are emotional effects that are commonly shared among those who suffer from STI's. There has recently been more research into the relationship between STI's and depression. Many who suffer from STI's claim feelings of isolation and loneliness, as well as fear of entering new relationships. There is certainly a social stigma associated with carrying sexually transmitted infections, and whatever emotions the infected person carries, these would have the potential to carry over into each partner in a sexual relationship.
Consider also the natural effects of anyterminal disease in a relationship. If one partner contracts a terminal disease, there is the added emotional trauma of knowing he or she could die. Finally, to take the letter of your question quite literally, you must also consider that if only one person "contracts" an STI within a relationship, and it is not contracted from the other partner, than a new door of negative emotional effects could opened with the assumption that a third party has been introduced into the relationship.
Finally, there are legal effects on relationships where one person has an STI. In many states, willingly entering into a sexual relationship without disclosing the presence of an STI to the other partner can mean criminal or civil liability for the infected partner, should the other choose to press charges.