Testing positive for the Virus doesn’t mean you are “infected” if you want to use that word in that way. It means that when they swab your sinuses they detect the virus. Your body can kill all the virus and a PCR test will pick up those shedding dead cells and pop a positive test. That’s why an antigen test is a better test, because it detects live virus in you. PCR testing doesn’t determine if your body is killing off the virus preventing you from getting sick, just detecting the presence of the cells. Also, you CAN get the measles, mumps, or rubella after 2 doses of the MMR vaccine.
There isn’t a single vaccine ever developed that prevents 100% of vaccinated people from getting sick, or transmitting the disease/virus they are vaccinated against to unvaccinated persons. None.