Whether you are monogamous or polyamorous, practicing safe sex is important. When a person is monogamous, they usually have one partner at a time. We tend to trust that our partners will not have sex with others outside the relationship. This does make it easier when wanting to make sure that we don't get an STD. Polyamory is slightly different.
In polyamory, there are multiple partners. If you are in a closed relationship, then you may have the same assumptions that a monogamous person has. You will believe that they will not give you an STD and you believe they don't have one when they came together with you. Short of ignorance, cheating or someone lying, this is a safe assumption.
Those who choose to have an open polyamorous relationship must be more diligent about their safety. When you have an open marriage or relationship, you can introduce multiple partners. Again, we like to assume that all is well, but the reality is that not everyone may be as healthy as you. Against all decency and common sense, some people won't tell their partners that they have an STD. Some are victims themselves, ignorant they have been infected with anything and blindly passing it on.
Another aspect of safe sex is birth control. Unless you and your partner(s) want children together, it is prudent to practice safe sex. There are a lot of myths about pregnancy. The long and short of it is that if you have sex, you run the risk of getting pregnant or getting your partner pregnant. No method of contraceptive is 100% fool proof.
For some, polyamory allows them to have multiple sexual relationships, some casual, some serious. Don't throw common sense out the window. Choose your partners carefully. You are not only risking your own health or future but that of your partners. They may not have sex with your boyfriend or girlfriend, but they will have sex with you. If you get and STD, they will probably get one as well. If a child is conceived, it can complicate things with your other partners.
If the unthinkable happens and you do become infected, don't let pride or shame keep you from doing the right thing. See a doctor and get treated as soon possible. Let any partners who may have been infected know so that they can get tested and treated if necessary. This is the right thing to do.
Remember, polyamory isn't about sex. It's about being in multiple loving relationships. But a by-product of any relationship can include sex. The more people you are romantically involved with, the more likely it is you will have multiple sex partners. Be smart and be safe.