The safety of condoms is directly related to the type of events that the user wants to get protected from. In the case of condoms and STDs or STIs, the first factor to understand is the difference between “perfect” and “typical” use. While “perfect use” means condoms are used following all instructions properly, “typical” use, refers to the usage which is typically achieved by the population. As one example, studies have evidenced that while unexpected pregnancy rates are ~2% in 12 months with perfect use, with inconsistent and incorrect use this rate goes as high as ~18%.[1]
In the case of STDs and STIs, one of the largest studies made sponsored by the NIH on condoms effectiveness to prevent STDs found that condoms (when used consistently) can reduce the risk of HIV, besides this, the range of reduction is as ample as ~35% to ~96%, giving a large margin to risk. (Additionally, if typical use is intended, this reduction becomes lower and I consequence the risk of contracting such disease is higher.)  In the case of other STDs, the panel stated that “the evidence for the effectiveness of condoms in preventing other STIs was considered to be insufficient”.[2]
Finally, is important to understand that prevention is key, according to the CDC “The most reliable ways to avoid transmission of STDs are to abstain from sexual activity, or to be in a long-term mutually monogamous relationship with an uninfected partner.”[3]