Myth busting: https://www.cdc.gov/media/releases/2021/s0806-vaccination-protection.html

"In today’s MMWR, a study of COVID-19 infections in Kentucky among people who were previously infected with SAR-CoV-2 shows that unvaccinated individuals are more than twice as likely to be reinfected with COVID-19 than those who were fully vaccinated after initially contracting the virus."